SU\G(𝔸)/K·U
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All published works (96)

Asymmetrical Trust Modeling for Human-Robot Swarm Interactions

2025-03-04
Daniel A. Williams , Airlie Chapman , Daniel R. Little +1 more

Hypersonic Glide Vehicle Shape and Trajectory Co-Design

2025-01-03
Andrew Lock , Glen Oberman , Ingo Jahn +4 more

Multi-Mission Codesign of a Hypersonic Vehicle Leading Edge With Heat Flux Constraints

2025-01-03
Chris van der Heide , Andrew Lock , Viv Bone +4 more

An Event-Triggered Framework for Trust-Mediated Human-Autonomy Interaction

2024-12-12
Daniel A. Williams , Airlie Chapman , Chris Manzie
Inspired by the increased cooperation between humans and autonomous systems, we present a new hybrid systems framework capturing the interconnected dynamics underlying these interactions. The framework accommodates models arising from … Inspired by the increased cooperation between humans and autonomous systems, we present a new hybrid systems framework capturing the interconnected dynamics underlying these interactions. The framework accommodates models arising from both the autonomous systems and cognitive psychology literature in order to represent key elements such as human trust in the autonomous system. The intermittent nature of human interactions are incorporated by asynchronous event-triggered sampling at the framework's human-autonomous system interfaces. We illustrate important considerations for tuning framework parameters by investigating a practical application to an autonomous robotic swarm search and rescue scenario. In this way, we demonstrate how the proposed framework may assist in designing more efficient and effective interactions between humans and autonomous systems.
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Temporal Planning via Interval Logic Satisfiability for Autonomous Systems

2024-06-13
Miquel Ramírez , Anubhav Singh , Peter J. Stuckey +1 more
Many automated planning methods and formulations rely on suitably designed abstractions or simplifications of the constrained dynamics associated with agents to attain computational scalability. We consider formulations of temporal planning … Many automated planning methods and formulations rely on suitably designed abstractions or simplifications of the constrained dynamics associated with agents to attain computational scalability. We consider formulations of temporal planning where intervals are associated with both action and fluent atoms, and relations between these are given as sentences in Allen's Interval Logic. We propose a notion of planning graphs that can account for complex concurrency relations between actions and fluents as a Constraint Programming (CP) model. We test an implementation of our algorithm on a state-of-the-art framework for CP and compare it with PDDL 2.1 planners that capture plans requiring complex concurrent interactions between agents. We demonstrate our algorithm outperforms existing PDDL 2.1 planners in the case studies. Still, scalability remains challenging when plans must comply with intricate concurrent interactions and the sequencing of actions.
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Contouring Error Bounded Control for Biaxial Switched Linear Systems

2024-04-08
Meng Yuan , Ye Wang , Chris Manzie +2 more
Biaxial motion control systems are used extensively in manufacturing and printing industries. To improve throughput and reduce machine cost, lightweight materials are being proposed in structural components but may result … Biaxial motion control systems are used extensively in manufacturing and printing industries. To improve throughput and reduce machine cost, lightweight materials are being proposed in structural components but may result in higher flexibility in the machine links. This flexibility is often position dependent and compromises precision of the end effector of the machine. To address the need for improved contouring accuracy in industrial machines with position-dependent structural flexibility, this paper introduces a novel contouring error-bounded control algorithm for biaxial switched linear systems. The proposed algorithm utilizes model predictive control to guarantee the satisfaction of state, input, and contouring error constraints for any admissible mode switching. In this paper, the switching signal remains unknown to the controller, although information about the minimum time the system is expected to stay in a specific mode is considered to be available. The proposed algorithm has the property of recursive feasibility and ensures the stability of the closed-loop system. The effectiveness of the proposed method is demonstrated by applying it to a high-fidelity simulation of a dual-drive industrial laser machine. The results show that the contouring error is successfully bounded within the given tolerance.
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A Control Barrier Function Composition Approach for Multi-Agent Systems in Marine Applications

2024-03-21
Yujia Yang , Chris Manzie , Ye Pu
The agents within a multi-agent system (MAS) operating in marine environments often need to utilize task payloads and avoid collisions in coordination, necessitating adherence to a set of relative-pose constraints, … The agents within a multi-agent system (MAS) operating in marine environments often need to utilize task payloads and avoid collisions in coordination, necessitating adherence to a set of relative-pose constraints, which may include field-of-view, line-of-sight, collision-avoidance, and range constraints. A nominal controller designed for reference tracking may not guarantee the marine MAS stays safe w.r.t. these constraints. To modify the nominal input as one that enforces safety, we introduce a framework to systematically encode the relative-pose constraints as nonsmooth control barrier functions (NCBFs) and combine them as a single NCBF using Boolean composition, which enables a simplified verification process compared to using the NCBFs individually. While other relative-pose constraint functions have explicit derivatives, the challenging line-of-sight constraint is encoded with the minimum distance function between the line-of-sight set and other agents, whose derivative is not explicit. Hence, existing safe control design methods that consider composite NCBFs cannot be applied. To address this challenge, we propose a novel quadratic program formulation based on the dual of the minimum distance problem and develop a new theory to ensure the resulting control input guarantees constraint satisfaction. Lastly, we validate the effectiveness of our proposed framework on a simulated large-scale marine MAS and a real-world marine MAS comprising one Unmanned Surface Vehicle and two Unmanned Underwater Vehicles.
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Gradient-enhanced deep Gaussian processes for multifidelity modelling

2024-02-25
Viv Bone , Chris van der Heide , Kieran Mackle +3 more
Multifidelity models integrate data from multiple sources to produce a single approximator for the underlying process. Dense low-fidelity samples are used to reduce interpolation error, while sparse high-fidelity samples are … Multifidelity models integrate data from multiple sources to produce a single approximator for the underlying process. Dense low-fidelity samples are used to reduce interpolation error, while sparse high-fidelity samples are used to compensate for bias or noise in the low-fidelity samples. Deep Gaussian processes (GPs) are attractive for multifidelity modelling as they are non-parametric, robust to overfitting, perform well for small datasets, and, critically, can capture nonlinear and input-dependent relationships between data of different fidelities. Many datasets naturally contain gradient data, especially when they are generated by computational models that are compatible with automatic differentiation or have adjoint solutions. Principally, this work extends deep GPs to incorporate gradient data. We demonstrate this method on an analytical test problem and a realistic partial differential equation problem, where we predict the aerodynamic coefficients of a hypersonic flight vehicle over a range of flight conditions and geometries. In both examples, the gradient-enhanced deep GP outperforms a gradient-enhanced linear GP model and their non-gradient-enhanced counterparts.
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A Hamilton-Jacobi-Bellman Approach to Ellipsoidal Approximations of Reachable Sets for Linear Time-Varying Systems

2024-01-01
Vincent Liu , Chris Manzie , Peter M. Dower
Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satisfaction … Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satisfaction in controller design or to verify that unsafe regions will be avoided. However, general-purpose methods for computing these sets suffer from the curse of dimensionality, which typically prohibits their use for systems with more than a small number of states, even if they are linear. In this paper, we demonstrate that viscosity supersolutions and subsolutions of a Hamilton-Jacobi-Bellman equation can be used to generate, respectively, under-approximating and over-approximating reachable sets for time-varying nonlinear systems. Based on this observation, we derive dynamics for a union and intersection of ellipsoidal sets that, respectively, under-approximate and over-approximate the reachable set for linear time-varying systems subject to an ellipsoidal input constraint and an ellipsoidal terminal (or initial) set. We demonstrate that the dynamics for these ellipsoids can be selected to ensure that their boundaries coincide with the boundary of the exact reachable set along a solution of the system. The ellipsoidal sets can be generated with polynomial computational complexity in the number of states, making our approximation scheme computationally tractable for continuous-time linear time-varying systems of relatively high dimension.
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A Hamilton-Jacobi-Bellman Approach to Ellipsoidal Approximations of Reachable Sets for Linear Time-Varying Systems

2024-01-01
Vincent Liu , Chris Manzie , Peter M. Dower
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Auction algorithm sensitivity for multi-robot task allocation

2023-09-06
Katie Clinch , Tony A. Wood , Chris Manzie
We consider the problem of finding a low-cost allocation and ordering of tasks between a team of robots in a d-dimensional, uncertain, landscape, and the sensitivity of this solution to … We consider the problem of finding a low-cost allocation and ordering of tasks between a team of robots in a d-dimensional, uncertain, landscape, and the sensitivity of this solution to changes in the cost function. Various algorithms have been shown to give a 2-approximation to the MinSum allocation problem. By analysing such an auction algorithm, we obtain intervals on each cost, such that any fluctuation of the costs within these intervals will result in the auction algorithm outputting the same solution.
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Collaborative Bearing Estimation Using Set Membership Methods

2023-06-28
Mohammad Reza Zamani , Jochen Trumpf , Chris Manzie
We consider the problem of collaborative bearing estimation using a method with historic roots in set theoretic estimation techniques. We refer to this method as the Convex Combination Ellipsoid (CCE) … We consider the problem of collaborative bearing estimation using a method with historic roots in set theoretic estimation techniques. We refer to this method as the Convex Combination Ellipsoid (CCE) method and show that it provides a less conservative covariance estimate than the well known Covariance Intersection (CI) method. The CCE method does not introduce additional uncertainty that was not already present in the prior estimates. Using our proposed approach for collaborative bearing estimation, the nonlinearity of the bearing measurement is captured as an uncertainty ellipsoid thereby avoiding the need for linearization or approximation via sampling procedures. Simulations are undertaken to evaluate the relative performance of the collaborative bearing estimation solution using the proposed (CCE) and typical (CI) methods.
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A Distributed Augmenting Path Approach for the Bottleneck Assignment Problem

2023-05-23
Mitchell Khoo , Tony A. Wood , Chris Manzie +1 more
We develop an algorithm to solve the Bottleneck Assignment Problem (BAP) that is amenable to having computation distributed over a network of agents. This consists of exploring how each component … We develop an algorithm to solve the Bottleneck Assignment Problem (BAP) that is amenable to having computation distributed over a network of agents. This consists of exploring how each component of the algorithm can be distributed, with a focus on one component in particular, i.e., the function to search for an augmenting path. An augmenting path is a common tool used in most BAP algorithms and poses a particular challenge for this distributed approach. Given this significance, we compare the properties of two different methods to search for an augmenting path in a bipartite graph. We evaluate the derived approaches with a simulation-based complexity investigation.
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Gradient free cooperative seeking of a moving source

2023-03-09
Michael Elad , Chris Manzie , Tony A. Wood +2 more
In this paper, we consider the optimisation of a time varying scalar field by a network of agents with no gradient information. We propose a composite control law, blending extremum … In this paper, we consider the optimisation of a time varying scalar field by a network of agents with no gradient information. We propose a composite control law, blending extremum seeking with formation control in order to converge to the extrema faster by minimising the gradient estimation error. By formalising the relationship between the formation and the gradient estimation error, we provide a novel analysis to prove the convergence of the network to a bounded neighbourhood of the field's time varying extrema. We assume the time-varying field satisfies the Polyak–Łojasiewicz inequality and the gradient is Lipschitz continuous at each iteration. Numerical studies and comparisons are provided to support the theoretical results.
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Sub-Optimal Moving Horizon Estimation in Feedback Control of Linear Constrained Systems

2023-01-01
Yujia Yang , Chris Manzie , Ye Pu
Moving horizon estimation (MHE) offers benefits relative to other estimation approaches by its ability to explicitly handle constraints, but suffers increased computation cost. To help enable MHE on platforms with … Moving horizon estimation (MHE) offers benefits relative to other estimation approaches by its ability to explicitly handle constraints, but suffers increased computation cost. To help enable MHE on platforms with limited computation power, we propose to solve the optimization problem underlying MHE sub-optimally for a fixed number of optimization iterations per time step. The stability of the closed-loop system is analyzed using the small-gain theorem by considering the closed-loop controlled system, the optimization algorithm dynamics, and the estimation error dynamics as three interconnected subsystems. By assuming incremental input/output-to-state stability ({\delta}- IOSS) of the system and imposing standard ISS conditions on the controller, we derive conditions on the iteration number such that the interconnected system is input-to-state stable (ISS) w.r.t. the external disturbances. A simulation using an MHE- MPC estimator-controller pair is used to validate the results.
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Collaborative Bearing Estimation Using Set Membership Methods

2023-01-01
Mohammad Reza Zamani , Jochen Trumpf , Chris Manzie
We consider the problem of collaborative bearing estimation using a method with historic roots in set theoretic estimation techniques. We refer to this method as the Convex Combination Ellipsoid (CCE) … We consider the problem of collaborative bearing estimation using a method with historic roots in set theoretic estimation techniques. We refer to this method as the Convex Combination Ellipsoid (CCE) method and show that it provides a less conservative covariance estimate than the well known Covariance Intersection (CI) method. The CCE method does not introduce additional uncertainty that was not already present in the prior estimates. Using our proposed approach for collaborative bearing estimation, the nonlinearity of the bearing measurement is captured as an uncertainty ellipsoid thereby avoiding the need for linearization or approximation via sampling procedures. Simulations are undertaken to evaluate the relative performance of the collaborative bearing estimation solution using the proposed (CCE) and typical (CI) methods.
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Auction algorithm sensitivity for multi-robot task allocation

2023-01-01
Katie Clinch , Tony A. Wood , Chris Manzie
We consider the problem of finding a low-cost allocation and ordering of tasks between a team of robots in a d-dimensional, uncertain, landscape, and the sensitivity of this solution to … We consider the problem of finding a low-cost allocation and ordering of tasks between a team of robots in a d-dimensional, uncertain, landscape, and the sensitivity of this solution to changes in the cost function. Various algorithms have been shown to give a 2-approximation to the MinSum allocation problem. By analysing such an auction algorithm, we obtain intervals on each cost, such that any fluctuation of the costs within these intervals will result in the auction algorithm outputting the same solution.
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Sub-Optimal Moving Horizon Estimation in Feedback Control of Linear Constrained Systems

2023-01-01
Yujia Yang , Chris Manzie , Ye Pu
Moving horizon estimation (MHE) offers benefits relative to other estimation approaches by its ability to explicitly handle constraints, but suffers increased computation cost. To help enable MHE on platforms with … Moving horizon estimation (MHE) offers benefits relative to other estimation approaches by its ability to explicitly handle constraints, but suffers increased computation cost. To help enable MHE on platforms with limited computation power, we propose to solve the optimization problem underlying MHE sub-optimally for a fixed number of optimization iterations per time step. The stability of the closed-loop system is analyzed using the small-gain theorem by considering the closed-loop controlled system, the optimization algorithm dynamics, and the estimation error dynamics as three interconnected subsystems. By assuming incremental input/output-to-state stability (δ-IOSS) of the system and imposing standard ISS conditions on the controller, we derive conditions on the iteration number such that the interconnected system is input-to-state stable (ISS) w.r.t. the external disturbances. A simulation with an MHE-MPC estimator-controller pair is used for validation.
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Stochastic Co-design of Storage and Control for Water Distribution Systems

2023-01-01
Ye Wang , Erik Weyer , Chris Manzie +2 more
Water distribution systems (WDSs) are typically designed with a conservative estimate of the ability of a control system to utilize the available infrastructure. The controller is designed and tuned after … Water distribution systems (WDSs) are typically designed with a conservative estimate of the ability of a control system to utilize the available infrastructure. The controller is designed and tuned after a WDS has been laid out, a methodology that may introduce unnecessary conservativeness in both system design and control, adversely impacting operational efficiency and increasing economic costs. To address these limitations, we introduce a method to simultaneously design infrastructure and develop control parameters, the co-design problem, with the aim of improving the overall efficiency of the system. Nevertheless, the co-design of a WDS is a challenging task given the presence of stochastic variables (e.g. water demands and electricity prices). In this paper, we propose a tractable stochastic co-design method to design the best tank size and optimal control parameters for WDS, where the expected operating costs are established based on Markov chain theory. We also give a theoretical result showing that the average long-run operating cost converges to the expected operating cost with probability~1. Furthermore, this method is not only applicable to greenfield projects for the co-design of WDSs but can also be utilized to improve the operations of existing WDSs in brownfield projects. The effectiveness and applicability of the co-design method are validated through three illustrative examples and a real-world case study in South Australia.
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Probabilistic Data Association for Semantic SLAM at Scale

2022-10-23
Michael Elad , Tyler Summers , Tony A. Wood +2 more
With advances in image processing and machine learning, it is now feasible to incorporate semantic information into the problem of simultaneous localisation and mapping (SLAM). Previously, SLAM was carried out … With advances in image processing and machine learning, it is now feasible to incorporate semantic information into the problem of simultaneous localisation and mapping (SLAM). Previously, SLAM was carried out using lower level geometric features (points, lines, and planes) which are often view-point dependent and error prone in visually repetitive environments. Semantic information can improve the ability to recognise previously visited locations, as well as maintain sparser maps for long term SLAM applications. However, SLAM in repetitive environments has the critical problem of assigning measurements to the landmarks which generated them. In this paper, we use k-best assignment enumeration to compute marginal assignment probabilities for each measurement landmark pair, in real time. We present numerical studies on the KITTI dataset to demonstrate the effectiveness and speed of the proposed framework.
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On Singular Perturbation for a Class of Discrete-Time Nonlinear Systems in the Presence of Limit Cycles of Fast Dynamics

2022-06-08
Hengchang Liu , Ying Tan , Tomislav Baček +5 more
This paper extends the existing singular perturbation results to a class of nonlinear discrete-time systems whose fast dynamics have limit cycles. By introducing the discrete-time reduced averaged system, the main … This paper extends the existing singular perturbation results to a class of nonlinear discrete-time systems whose fast dynamics have limit cycles. By introducing the discrete-time reduced averaged system, the main result (Theorem 1) shows that for a given fixed time interval, the solutions of the original system can be made arbitrarily close to the solutions of the reduced averaged system and the boundary layer system. From this result, the stability properties of the original system are obtained from the stability properties of the reduced averaged system and the boundary layer system. Simulation results support the theoretical findings.

Individual and Team Trust Preferences for Robotic Swarm Behaviors

2022-06-08
Elena M. Vella , Daniel A. Williams , Airlie Chapman +1 more
Trust between humans and multi-agent robotic swarms may be analyzed using human preferences. These preferences are expressed by an individual as a sequence of ordered comparisons between pairs of swarm … Trust between humans and multi-agent robotic swarms may be analyzed using human preferences. These preferences are expressed by an individual as a sequence of ordered comparisons between pairs of swarm behaviors. An individual's preference graph can be formed from this sequence. In addition, swarm behaviors may be mapped to a feature vector space. We formulate a linear optimization problem to locate a trusted behavior in the feature space. Extending to human teams, we define a novel distinctiveness metric using a sparse optimization formulation to cluster similar individuals from a collection of individuals' labeled pairwise preferences. The case of anonymized unlabeled pairwise preferences is also examined to find the average trusted behavior and minimum covariance bound, providing insights into group cohesion. A user study was conducted, with results suggesting that individuals with similar trust profiles can be clustered to facilitate human-swarm teaming.
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A greedy and distributable approach to the Lexicographic Bottleneck Assignment Problem with conditions on exactness

2022-03-22
Mitchell Khoo , Tony A. Wood , Chris Manzie +1 more
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Sensitivity analysis for bottleneck assignment problems

2022-02-23
Elad Michael , Tony A. Wood , Chris Manzie +1 more
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Robust distributed model predictive control of linear systems: Analysis and synthesis

2022-01-13
Ye Wang , Chris Manzie
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Individual and Team Trust Preferences for Robotic Swarm Behaviors

2022-01-01
Elena M. Vella , Daniel A. Williams , Airlie Chapman +1 more
Trust between humans and multi-agent robotic swarms may be analyzed using human preferences. These preferences are expressed by an individual as a sequence of ordered comparisons between pairs of swarm … Trust between humans and multi-agent robotic swarms may be analyzed using human preferences. These preferences are expressed by an individual as a sequence of ordered comparisons between pairs of swarm behaviors. An individual's preference graph can be formed from this sequence. In addition, swarm behaviors may be mapped to a feature vector space. We formulate a linear optimization problem to locate a trusted behavior in the feature space. Extending to human teams, we define a novel distinctiveness metric using a sparse optimization formulation to cluster similar individuals from a collection of individuals' labeled pairwise preferences. The case of anonymized unlabeled pairwise preferences is also examined to find the average trusted behavior and minimum covariance bound, providing insights into group cohesion. A user study was conducted, with results suggesting that individuals with similar trust profiles can be clustered to facilitate human-swarm teaming.
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Probabilistic Data Association for Semantic SLAM at Scale

2022-01-01
Michael Elad , Tyler Summers , Tony A. Wood +2 more
With advances in image processing and machine learning, it is now feasible to incorporate semantic information into the problem of simultaneous localisation and mapping (SLAM). Previously, SLAM was carried out … With advances in image processing and machine learning, it is now feasible to incorporate semantic information into the problem of simultaneous localisation and mapping (SLAM). Previously, SLAM was carried out using lower level geometric features (points, lines, and planes) which are often view-point dependent and error prone in visually repetitive environments. Semantic information can improve the ability to recognise previously visited locations, as well as maintain sparser maps for long term SLAM applications. However, SLAM in repetitive environments has the critical problem of assigning measurements to the landmarks which generated them. In this paper, we use k-best assignment enumeration to compute marginal assignment probabilities for each measurement landmark pair, in real time. We present numerical studies on the KITTI dataset to demonstrate the effectiveness and speed of the proposed framework.
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Gradient Free Cooperative Seeking of a Moving Source

2022-01-01
Michael Elad , Chris Manzie , Tony A. Wood +2 more
In this paper, we consider the optimisation of a time varying scalar field by a network of agents with no gradient information. We propose a composite control law, blending extremum … In this paper, we consider the optimisation of a time varying scalar field by a network of agents with no gradient information. We propose a composite control law, blending extremum seeking with formation control in order to converge to the extrema faster by minimising the gradient estimation error. By formalising the relationship between the formation and the gradient estimation error, we provide a novel analysis to prove the convergence of the network to a bounded neighbourhood of the field's time varying extrema. We assume the time-varying field satisfies the Polyak Lojasiewicz inequality and the gradient is Lipschitz continuous at each iteration. Numerical studies and comparisons are provided to support the theoretical results.
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Data-driven Predictive Tracking Control based on Koopman Operators

2022-01-01
Ye Wang , Yujia Yang , Ye Pu +1 more
Constraint handling during tracking operations is at the core of many real-world control implementations and is well understood when dynamic models of the underlying system exist, yet becomes more challenging … Constraint handling during tracking operations is at the core of many real-world control implementations and is well understood when dynamic models of the underlying system exist, yet becomes more challenging when data-driven models are used to describe the nonlinear system at hand. We seek to combine the nonlinear modeling capabilities of a wide class of neural networks with the constraint-handling guarantees of model predictive control (MPC) in a rigorous and online computationally tractable framework. The class of networks considered can be captured using Koopman operators, and are integrated into a Koopman-based tracking MPC (KTMPC) for nonlinear systems to track piecewise constant references. The effect of model mismatch between original nonlinear dynamics and its trained Koopman linear model is handled by using a constraint tightening approach in the proposed tracking MPC strategy. By choosing two Lyapunov functions, we prove that solution is recursively feasible and input-to-state stable to a neighborhood of both online and offline optimal reachable steady outputs in the presence of bounded modeling errors under mild assumptions. Finally, we demonstrate the results on a numerical example, before applying the proposed approach to the problem of reference tracking by an autonomous ground vehicle.
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Explicit Time-Optimal Speed Profiles for Planar Paths with Monotone Curvature

2022-01-01
Daniel Selvaratnam , Michael Cantoni , Chris Manzie
Minimum-time speed profiles are constructed for planar paths with smooth strictly-monotonic signed curvature, subject to constraints on velocity, normal acceleration and tangential acceleration. The construction is explicit and exact, and … Minimum-time speed profiles are constructed for planar paths with smooth strictly-monotonic signed curvature, subject to constraints on velocity, normal acceleration and tangential acceleration. The construction is explicit and exact, and global optimality is rigorously established from first principles under mild regularity conditions on the path. Free, fixed, and inequality-constrained boundary speeds are all accommodated. Numerical implementation is straightforward.
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Real-Time Distributed Model Predictive Control with Limited Communication Data Rates

2022-01-01
Yujia Yang , Ye Wang , Chris Manzie +1 more
The application of distributed model predictive controllers (DMPC) for multi-agent systems (MASs) necessitates communication between agents, yet the consequence of communication data rates is typically overlooked. This work focuses on … The application of distributed model predictive controllers (DMPC) for multi-agent systems (MASs) necessitates communication between agents, yet the consequence of communication data rates is typically overlooked. This work focuses on developing stability-guaranteed control methods for MASs with limited data rates. Initially, a distributed optimization algorithm with dynamic quantization is considered for solving the DMPC problem. Due to the limited data rate, the optimization process suffers from inexact iterations caused by quantization noise and premature termination, leading to sub-optimal solutions. In response, we propose a novel real-time DMPC framework with a quantization refinement scheme that updates the quantization parameters on-line so that both the quantization noise and the optimization sub-optimality decrease asymptotically. To facilitate the stability analysis, we treat the sub-optimally controlled MAS, the quantization refinement scheme, and the optimization process as three interconnected subsystems. The cyclic-small-gain theorem is used to derive sufficient conditions on the quantization parameters for guaranteeing the stability of the system under a limited data rate. Finally, the proposed algorithm and theoretical findings are demonstrated in a multi-AUV formation control example.
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Lazy Probabilistic Roadmaps Revisited

2022-01-01
Miquel Ramírez , Daniel Selvaratnam , Chris Manzie
This paper describes a revision of the classic Lazy Probabilistic Roadmaps algorithm (Lazy PRM), that results from pairing PRM and a novel Branch-and-Cut (BC) algorithm. Cuts are dynamically generated constraints … This paper describes a revision of the classic Lazy Probabilistic Roadmaps algorithm (Lazy PRM), that results from pairing PRM and a novel Branch-and-Cut (BC) algorithm. Cuts are dynamically generated constraints that are imposed on minimum cost paths over the geometric graphs selected by PRM. Cuts eliminate paths that cannot be mapped into smooth plans that satisfy suitably defined kinematic constraints. We generate candidate smooth plans by fitting splines to vertices in minimum-cost path. Plans are validated with a recently proposed algorithm that maps them into finite traces, without need to choose a fixed discretization step. Trace elements exactly describe when plans cross constraint boundaries modulo arithmetic precision. We evaluate several planners using our methods over the recently proposed BARN benchmark, and we report evidence of the scalability of our approach.
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Asynchronous Event-Triggered Control for Non-Linear Systems

2022-01-01
Daniel Williams , Airlie Chapman , Chris Manzie
With the increasing ubiquity of networked control systems, various strategies for sampling constituent subsystems' outputs have emerged. In contrast with periodic sampling, event-triggered control provides a way to efficiently sample … With the increasing ubiquity of networked control systems, various strategies for sampling constituent subsystems' outputs have emerged. In contrast with periodic sampling, event-triggered control provides a way to efficiently sample a subsystem and conserve network resource usage, by triggering an update only when a state-dependent error threshold is satisfied. Herein we describe a novel scheme for asynchronous event-triggered measurement and control (ETC) of a nonlinear plant using sampler subsystems with hybrid dynamics. We extend existing ETC literature by adopting a more general representation of the sampler subsystem dynamics that do not require trigger periodicity or simultaneity, thus accommodating different sampling schemes for both synchronous and asynchronous ETC applications. We ensure that the plant and controller trigger rules are not susceptible to Zeno behavior by employing auxiliary timer variables in conjunction with state-dependent error thresholds. We conclude with a numerical example in order to illustrate important practical considerations when applying such schemes.
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Zeroth-Order Optimization on Subsets of Symmetric Matrices With Application to MPC Tuning

2021-11-09
Alejandro I. Maass , Chris Manzie , Iman Shames +1 more
This article provides a zeroth-order optimization framework for nonsmooth and possibly nonconvex cost functions with matrix parameters that are real and symmetric. We provide complexity bounds on the number of … This article provides a zeroth-order optimization framework for nonsmooth and possibly nonconvex cost functions with matrix parameters that are real and symmetric. We provide complexity bounds on the number of iterations required to ensure a given accuracy level for both the convex and nonconvex cases. The derived complexity bounds for the convex case are less conservative than available bounds in the literature since we exploit the symmetric structure of the underlying matrix space. Moreover, the nonconvex complexity bounds are novel for the class of optimization problems that we consider. The utility of the framework is evident in the suite of applications that use symmetric matrices as tuning parameters. Of primary interest here is the challenge of tuning the gain matrices in model predictive controllers, as this is a challenge known to be inhibiting the industrial implementation of these architectures. To demonstrate the framework, we consider the problem of MIMO diesel air-path control and implement the framework iteratively "in-the-loop" to reduce tracking error on the output channels. Both simulations and experimental results are included to illustrate the effectiveness of the proposed framework over different engine drive cycles.

Temporal Logic Planning for Minimum-Time Positioning of Multiple Threat-Seduction Decoys.

2021-06-17
Tony A. Wood , Mitchell Khoo , Michael Elad +2 more
Reusable decoys offer a cost-effective alternative to the single-use hardware commonly applied to protect surface assets from threats. Such decoys portray fake assets to lure threats away from the true … Reusable decoys offer a cost-effective alternative to the single-use hardware commonly applied to protect surface assets from threats. Such decoys portray fake assets to lure threats away from the true asset. To deceive a threat, a decoy first has to position itself such that it can break the radar lock. Considering multiple simultaneous threats, this paper introduces an approach for controlling multiple decoys to minimise the time required to break the locks of all the threats. The method includes the optimal allocation of one decoy to every threat with an assignment procedure that provides local position constraints to guarantee collision avoidance and thereby decouples the control of the decoys. A crude model of a decoy with uncertainty is considered for motion planning. The task of a decoy reaching a state in which the lock of the assigned threat can be broken is formulated as a temporal logic specification. To this end, the requirements to complete the task are modelled as time-varying set-membership constraints. The temporal and logical combination of the constraints is encoded in a mixed-integer optimisation problem. To demonstrate the results a simulated case study is provided.
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Ordinal Optimisation and the Offline Multiple Noisy Secretary Problem

2021-06-02
Robert Chin , Jonathan E. Rowe , Iman Shames +2 more
We study the success probability for a variant of the secretary problem, with noisy observations and multiple offline selection. Our formulation emulates, and is motivated by, problems involving noisy selection … We study the success probability for a variant of the secretary problem, with noisy observations and multiple offline selection. Our formulation emulates, and is motivated by, problems involving noisy selection arising in the disciplines of stochastic simulation and simulation-based optimisation. In addition, we employ the philosophy of ordinal optimisation - involving an ordinal selection rule, and a percentile notion of goal softening for the success probability. As a result, it is shown that the success probability only depends on the underlying copula of the problem. Other general properties for the success probability are also presented. Specialising to the case of Gaussian copulas, we also derive an analytic lower bound for the success probability, which may then be inverted to find sufficiently large sample sizes that guarantee a high success probability arbitrarily close to one.
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Real-time Distributed MPC for Multiple Underwater Vehicles with Limited Communication Data-rates

2021-05-25
Yujia Yang , Ye Wang , Chris Manzie +1 more
Controlling a fleet of autonomous underwater vehicles can be challenging due to low data-rate communication between agents. This paper proposes a real-time framework with an optimally designed progressive quantization scheme … Controlling a fleet of autonomous underwater vehicles can be challenging due to low data-rate communication between agents. This paper proposes a real-time framework with an optimally designed progressive quantization scheme to addresses this challenge. The proposed framework consists of two stages: an off-line stage where the optimal quantization design is obtained considering the limited data-rate, i.e., a limited number of bits transmitted per time step; and an on-line stage based on a distributed model predictive control formulation and a distributed optimization algorithm with progressive quantization. Recursive feasibility and stability of the closed-loop systems are analyzed, and simulations are used to demonstrate the proposed approach, as well as the theoretical findings.
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Minimizing Pumping Energy Cost in Real-Time Operations of Water Distribution Systems Using Economic Model Predictive Control

2021-05-13
Ye Wang , Kevin Too Yok , Wenyan Wu +3 more
Optimizing pump operations is a challenging task for real-time management of water distribution systems (WDS). With suitable pump scheduling, pumping costs can be significantly reduced. In this research, a novel … Optimizing pump operations is a challenging task for real-time management of water distribution systems (WDS). With suitable pump scheduling, pumping costs can be significantly reduced. In this research, a novel economic model predictive control (EMPC) framework for real-time management of WDS is proposed. Optimal pump operations are selected based on predicted system behavior over a receding time horizon with the aim to minimize the total pumping energy cost. Time-varying electricity tariffs are considered while all the required water demands are satisfied. The novelty of this framework is to choose the number of pumps to operate in each pump station as decision variables in order to optimize the total pumping energy costs. By using integer programming, the proposed EMPC is applied to a benchmark case study, the Richmond Pruned network. The simulation with an EPANET hydraulic simulator is implemented. Moreover, a comparison of the results obtained using the proposed EMPC with those obtained using trigger-level control demonstrates significant economic benefits of the proposed EMPC.
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Practical exponential stability and closeness of solutions for singularly perturbed systems via averaging

2021-01-25
Mohammad Deghat , Saeed Ahmadizadeh , Dragan Nešić +1 more
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Interior Point Differential Dynamic Programming

2021-01-21
Andrei Pavlov , Iman Shames , Chris Manzie
This brief introduces a novel differential dynamic programming (DDP) algorithm for solving discrete-time finite-horizon optimal control problems with inequality constraints. Two variants, namely feasible- and infeasible-IPDDP algorithms, are developed using … This brief introduces a novel differential dynamic programming (DDP) algorithm for solving discrete-time finite-horizon optimal control problems with inequality constraints. Two variants, namely feasible- and infeasible-IPDDP algorithms, are developed using a primal–dual interior-point methodology, and their local quadratic convergence properties are characterized. We show that the stationary points of the algorithms are the perturbed KKT points, and thus can be moved arbitrarily close to a locally optimal solution. Being free from the burden of the active-set methods, it can handle nonlinear state and input inequality constraints without a discernible increase in its computational complexity relative to the unconstrained case. The performance of the proposed algorithms is demonstrated using numerical experiments on three different problems: control-limited inverted pendulum, car-parking, and unicycle motion control and obstacle avoidance.
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A Sequential Learning Algorithm for Probabilistically Robust Controller Tuning

2021-01-01
Robert Chin , Chris Manzie , Iman Shames +2 more
We introduce a sequential learning algorithm to address a robust controller tuning problem, which in effect, finds (with high probability) a candidate solution satisfying the internal performance constraint to a … We introduce a sequential learning algorithm to address a robust controller tuning problem, which in effect, finds (with high probability) a candidate solution satisfying the internal performance constraint to a chance-constrained program which has black-box functions. The algorithm leverages ideas from the areas of randomised algorithms and ordinal optimisation, and also draws comparisons with the scenario approach; these have all been previously applied to finding approximate solutions for difficult design problems. By exploiting statistical correlations through black-box sampling, we formally prove that our algorithm yields a controller meeting the prescribed probabilistic performance specification. Additionally, we characterise the computational requirement of the algorithm with a probabilistic lower bound on the algorithm's stopping time. To validate our work, the algorithm is then demonstrated for tuning model predictive controllers on a diesel engine air-path across a fleet of vehicles. The algorithm successfully tuned a single controller to meet a desired tracking error performance, even in the presence of the plant uncertainty inherent across the fleet. Moreover, the algorithm was shown to exhibit a sample complexity comparable to the scenario approach.
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Ordinal Optimisation and the Offline Multiple Noisy Secretary Problem

2021-01-01
Robert Chin , Jonathan E. Rowe , Iman Shames +2 more
We study the success probability for a variant of the secretary problem, with noisy observations and multiple offline selection. Our formulation emulates, and is motivated by, problems involving noisy selection … We study the success probability for a variant of the secretary problem, with noisy observations and multiple offline selection. Our formulation emulates, and is motivated by, problems involving noisy selection arising in the disciplines of stochastic simulation and simulation-based optimisation. In addition, we employ the philosophy of ordinal optimisation - involving an ordinal selection rule, and a percentile notion of goal softening for the success probability. As a result, it is shown that the success probability only depends on the underlying copula of the problem. Other general properties for the success probability are also presented. Specialising to the case of Gaussian copulas, we also derive an analytic lower bound for the success probability, which may then be inverted to find sufficiently large sample sizes that guarantee a high success probability arbitrarily close to one.
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Zeroth-order optimisation on subsets of symmetric matrices with application to MPC tuning

2021-01-01
Alejandro I. Maass , Chris Manzie , Iman Shames +1 more
This paper provides a zeroth-order optimisation framework for non-smooth and possibly non-convex cost functions with matrix parameters that are real and symmetric. We provide complexity bounds on the number of … This paper provides a zeroth-order optimisation framework for non-smooth and possibly non-convex cost functions with matrix parameters that are real and symmetric. We provide complexity bounds on the number of iterations required to ensure a given accuracy level for both the convex and non-convex case. The derived complexity bounds for the convex case are less conservative than available bounds in the literature since we exploit the symmetric structure of the underlying matrix space. Moreover, the non-convex complexity bounds are novel for the class of optimisation problems we consider. The utility of the framework is evident in the suite of applications that use symmetric matrices as tuning parameters. Of primary interest here is the challenge of tuning the gain matrices in model predictive controllers, as this is a challenge known to be inhibiting industrial implementation of these architectures. To demonstrate the framework we consider the problem of MIMO diesel air-path control, and consider implementing the framework iteratively ``in-the-loop'' to reduce tracking error on the output channels. Both simulations and experimental results are included to illustrate the effectiveness of the proposed framework over different engine drive cycles.
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Temporal Logic Planning for Minimum-Time Positioning of Multiple Threat-Seduction Decoys

2021-01-01
Tony A. Wood , Mitchell Khoo , Michael Elad +2 more
Reusable decoys offer a cost-effective alternative to the single-use hardware commonly applied to protect surface assets from threats. Such decoys portray fake assets to lure threats away from the true … Reusable decoys offer a cost-effective alternative to the single-use hardware commonly applied to protect surface assets from threats. Such decoys portray fake assets to lure threats away from the true asset. To deceive a threat, a decoy first has to position itself such that it can break the radar lock. Considering multiple simultaneous threats, this paper introduces an approach for controlling multiple decoys to minimise the time required to break the locks of all the threats. The method includes the optimal allocation of one decoy to every threat with an assignment procedure that provides local position constraints to guarantee collision avoidance and thereby decouples the control of the decoys. A crude model of a decoy with uncertainty is considered for motion planning. The task of a decoy reaching a state in which the lock of the assigned threat can be broken is formulated as a temporal logic specification. To this end, the requirements to complete the task are modelled as time-varying set-membership constraints. The temporal and logical combination of the constraints is encoded in a mixed-integer optimisation problem. To demonstrate the results a simulated case study is provided.
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Sensitivity Analysis for Bottleneck Assignment Problems

2021-01-01
Michael Elad , Tony A. Wood , Chris Manzie +1 more
In assignment problems, decision makers are often interested in not only the optimal assignment, but also the sensitivity of the optimal assignment to perturbations in the assignment weights. Typically, only … In assignment problems, decision makers are often interested in not only the optimal assignment, but also the sensitivity of the optimal assignment to perturbations in the assignment weights. Typically, only perturbations to individual assignment weights are considered. We present a novel extension of the traditional sensitivity analysis by allowing for simultaneous variations in all assignment weights. Focusing on the bottleneck assignment problem, we provide two different methods of quantifying the sensitivity of the optimal assignment, and present algorithms for each. Numerical examples as well as a discussion of the complexity for all algorithms are provided.
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Task-Space Synergies for Reaching Using Upper-Limb Prostheses

2020-11-05
Ricardo Garcia-Rosas , Denny Oetomo , Chris Manzie +2 more
Synergistic prostheses enable the coordinated movement of the human-prosthetic arm, as required by activities of daily living. This is achieved by coupling the motion of the prosthesis to the human … Synergistic prostheses enable the coordinated movement of the human-prosthetic arm, as required by activities of daily living. This is achieved by coupling the motion of the prosthesis to the human command, such as the residual limb movement in motion-based interfaces. Previous studies demonstrated that developing human-prosthetic synergies in joint-space must consider individual motor behaviour and the intended task to be performed, requiring personalisation and task calibration. In this work, an alternative synergy-based strategy, utilising a synergistic relationship expressed in task-space, is proposed. This task-space synergy has the potential to replace the need for personalisation and task calibration with a model-based approach requiring knowledge of the individual user's arm kinematics, the anticipated hand motion during the task and voluntary information from the prosthetic user. The proposed method is compared with surface electromyography-based and joint-space synergy-based prosthetic interfaces in a study of motor behaviour and task performance on able-bodied subjects using a VR-based transhumeral prosthesis. Experimental results showed that for a set of forward reaching tasks the proposed task-space synergy achieves comparable performance to joint-space synergies without the need to rely on time-consuming calibration processes or human motor learning. Case study results with an amputee subject motivate the further development of the proposed task-space synergy method.
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Online Zeroth-order Optimisation on Riemannian Manifolds

2020-10-01
Alejandro I. Maass , Chris Manzie , Dragan Nešić +2 more
We study numerical optimisation algorithms that use zeroth-order information to minimise time-varying geodesically-convex cost functions on Riemannian manifolds. In the Euclidean setting, zeroth-order algorithms have received a lot of attention … We study numerical optimisation algorithms that use zeroth-order information to minimise time-varying geodesically-convex cost functions on Riemannian manifolds. In the Euclidean setting, zeroth-order algorithms have received a lot of attention in both the time-varying and time-invariant case. However, the extension to Riemannian manifolds is much less developed. We focus on Hadamard manifolds, which are a special class of Riemannian manifolds with global nonpositive curvature that offer convenient grounds for the generalisation of convexity notions. Specifically, we derive bounds on the expected instantaneous tracking error, and we provide algorithm parameter values that minimise a metric of performance. Our results illustrate how the manifold geometry in terms of the sectional curvature affects these bounds. To the best of our knowledge, these are the first error bounds for online zeroth-order Riemannian optimisation. Lastly, via numerical simulations, we demonstrate the applicability of our algorithm on an online Karcher mean problem.
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Online Zeroth-order Optimisation on Hadamard Manifolds

2020-10-01
Alejandro I. Maass , Chris Manzie , Dragan Nešić +2 more
We study numerical optimisation algorithms that use zeroth-order information to minimise time-varying geodesically-convex cost functions on Riemannian manifolds. In the Euclidean setting, zeroth-order algorithms have received a lot of attention … We study numerical optimisation algorithms that use zeroth-order information to minimise time-varying geodesically-convex cost functions on Riemannian manifolds. In the Euclidean setting, zeroth-order algorithms have received a lot of attention in both the time-varying and time-invariant case. However, the extension to Riemannian manifolds is much less developed. We focus on Hadamard manifolds, which are a special class of Riemannian manifolds with global nonpositive curvature that offer convenient grounds for the generalisation of convexity notions. Specifically, we derive bounds on the expected instantaneous tracking error, and we provide algorithm parameter values that minimise the algorithm's performance. Our results illustrate how the manifold geometry in terms of the sectional curvature affects these bounds. Additionally, we provide dynamic regret bounds for this online optimisation setting. To the best of our knowledge, these are the first bounds on tracking error and dynamic regret for online zeroth-order Riemannian optimisation. Lastly, via numerical simulations, we demonstrate the applicability of our algorithm on an online Karcher mean problem.
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A Greedy and Distributable Approach to the Lexicographical Bottleneck Assignment Problem with Conditions on Exactness

2020-08-28
Mitchell Khoo , Tony A. Wood , Chris Manzie +1 more
The Lexicographical Bottleneck Assignment Problem (LexBAP) typically requires centralised computation with quartic complexity. We consider the Sequential Bottleneck Assignment Problem (SeqBAP) and its relationship to the LexBAP. By exploiting structure … The Lexicographical Bottleneck Assignment Problem (LexBAP) typically requires centralised computation with quartic complexity. We consider the Sequential Bottleneck Assignment Problem (SeqBAP) and its relationship to the LexBAP. By exploiting structure of the Bottleneck Assignment Problem, we derive an algorithm that solves the SeqBAP with cubic complexity. We analyse conditions for which solutions sets of the LexBAP and the SeqBAP coincide. When these conditions hold, the algorithm solves the LexBAP with computation that can be distributed over a network of agents.
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Exploiting Structure in the Bottleneck Assignment Problem

2020-08-25
Mitchell Khoo , Tony A. Wood , Chris Manzie +1 more
An assignment problem arises when there exists a set of tasks that must be allocated to a set of agents. The bottleneck assignment problem (BAP) has the objective of minimising … An assignment problem arises when there exists a set of tasks that must be allocated to a set of agents. The bottleneck assignment problem (BAP) has the objective of minimising the most costly allocation of a task to an agent. Under certain conditions the structure of the BAP can be exploited such that subgroups of tasks are assigned separately with lower complexity and then merged to form a combined assignment. In particular, we discuss merging the assignments from two separate BAPs and use the solution of the subproblems to bound the solution of the combined problem. We also provide conditions for cases where the solution of the subproblems produces an exact solution to the BAP over the combined problem. We then introduce a particular algorithm for solving the BAP that takes advantage of this insight. The methods are demonstrated in a numerical case study.
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Common Coauthors

Coauthor Papers Together
Iman Shames 39
Tony A. Wood 25
Dragan Nešić 16
Denny Oetomo 14
Michael Elad 13
Peter Choong 13
Mitchell Khoo 11
Wenceslao Shaw Cortez 10
Hayato Nakada 9
Robert Chin 8
Alejandro I. Maass 7
Ye Pu 7
Jonathan E. Rowe 7
Airlie Chapman 5
Peter M. Dower 5
Ye Wang 5
Yujia Yang 4
Gokul S. Sankar 4
Mohammad Deghat 4
Ying Tan 4
Daniel Zelazo 4
Saeed Ahmadizadeh 4
William H. Moase 4
Rohan C. Shekhar 4
Vincent Bachtiar 3
Eric C. Kerrigan 3
Ye Wang 3
Viv Bone 3
Daniel A. Williams 3
Takeshi Sano 3
Ingo Jahn 3
Yujia Yang 3
Ricardo Garcia-Rosas 3
Jonathan H. Manton 3
Chris van der Heide 3
Elena M. Vella 2
Miquel Ramírez 2
Erik Weyer 2
Nalika Ulapane 2
Mohammad Reza Zamani 2
Katie Clinch 2
Andrei Pavlov 2
Jochen Trumpf 2
Angus R. Simpson 2
Tyler Summers 2
Andrew Lock 2
Kieran Mackle 2
Takeshi Sano 2
Elad Michael 2
Daniel Selvaratnam 2

Commonly Cited References

Fast Calibration of a Robust Model Predictive Controller for Diesel Engine Airpath

2019-06-07
Gokul S. Sankar , Rohan C. Shekhar , Chris Manzie +2 more
A significant challenge in the development of control systems for diesel airpath applications is to tune the controller parameters to achieve satisfactory output performance, especially while adhering to input and … A significant challenge in the development of control systems for diesel airpath applications is to tune the controller parameters to achieve satisfactory output performance, especially while adhering to input and safety constraints in the presence of unknown system disturbances. Model-based control techniques, such as model predictive control (MPC), have been successfully applied to multivariable and highly nonlinear systems, such as diesel engines, while considering operational constraints. However, efficient calibration of typical implementations of MPC is hindered by the high number of tuning parameters and their nonintuitive correlation with the output response. In this paper, the number of effective tuning parameters is reduced through suitable structural modifications to the controller formulation and an appropriate redesign of the MPC cost function to aid rapid calibration. Furthermore, a constraint tighteninglike approach is augmented to the control architecture to provide robustness guarantees in the face of uncertainties. A switched linear time-invariant MPC strategy with recursive feasibility guarantees during controller switching is proposed to handle transient operation of the engine. The robust controller is first implemented on a high-fidelity simulation environment, with a comprehensive investigation of its calibration to achieve desired transient response under step changes in the fuelling rate. An experimental study then validates and highlights the performance of the proposed controller architecture for the selected tunings of the calibration parameters for fuelling steps and over drive cycles.
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SENSITIVITY ANALYSIS OF OBJECTIVE FUNCTION COEFFICIENTS OF THE ASSIGNMENT PROBLEM

2007-04-01
Chi-Jen Lin , Ue‐Pyng Wen
Information of sensitivity analysis, in a linear programming problem, is usually more important than the optimal solution itself. However, traditional sensitivity analysis, which perturbs exactly one coefficient and then determines … Information of sensitivity analysis, in a linear programming problem, is usually more important than the optimal solution itself. However, traditional sensitivity analysis, which perturbs exactly one coefficient and then determines the range preserving the optimality of the current optimal base, is impractical for the assignment problem. An optimal basic solution of the assignment problem is inherently degenerate, so it may be that the optimal base has changed but the optimal assignment remains unchanged. Furthermore, elements of a column (or row) in a cost matrix of assignment problem are usually closely related and change simultaneously, not uniquely. This paper focuses on two kinds of sensitivity analyses for the assignment problem. One is to determine the sensitivity range, over which the current optimal assignment or all the optimal assignments remain optimal, while perturbing the elements of one column (or row) in a cost matrix of the assignment problem simultaneously but dependently. The other is to perturb elements of one column (or row) in a cost matrix of the assignment problem simultaneously but independently. Numerical illustrations are presented to demonstrate that the approaches are useful in practice.

Control Barrier Function Based Quadratic Programs for Safety Critical Systems

2016-12-13
Aaron D. Ames , Xiangru Xu , Jessy W. Grizzle +1 more
Safety critical systems involve the tight coupling between potentially conflicting control objectives and safety constraints. As a means of creating a formal framework for controlling systems of this form, and … Safety critical systems involve the tight coupling between potentially conflicting control objectives and safety constraints. As a means of creating a formal framework for controlling systems of this form, and with a view toward automotive applications, this paper develops a methodology that allows safety conditions-expressed as control barrier functions-to be unified with performance objectives-expressed as control Lyapunov functions-in the context of real-time optimization-based controllers. Safety conditions are specified in terms of forward invariance of a set, and are verified via two novel generalizations of barrier functions; in each case, the existence of a barrier function satisfying Lyapunov-like conditions implies forward invariance of the set, and the relationship between these two classes of barrier functions is characterized. In addition, each of these formulations yields a notion of control barrier function (CBF), providing inequality constraints in the control input that, when satisfied, again imply forward invariance of the set. Through these constructions, CBFs can naturally be unified with control Lyapunov functions (CLFs) in the context of a quadratic program (QP); this allows for the achievement of control objectives (represented by CLFs) subject to conditions on the admissible states of the system (represented by CBFs). The mediation of safety and performance through a QP is demonstrated on adaptive cruise control and lane keeping, two automotive control problems that present both safety and performance considerations coupled with actuator bounds.
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Collision Avoidance Based on Robust Lexicographic Task Assignment

2020-07-14
Tony A. Wood , Mitchell Khoo , Elad Michael +2 more
Traditional task assignment approaches for multi-agent motion control do not take the possibility of collisions into account. This can lead to challenging requirements for path planning. We derive an assignment … Traditional task assignment approaches for multi-agent motion control do not take the possibility of collisions into account. This can lead to challenging requirements for path planning. We derive an assignment method that not only minimises the largest distance between an agent and its assigned destination but also provides local constraints for guaranteed collision avoidance. To this end, we introduce a sequential bottleneck optimisation problem and define a notion of robustness of an optimising assignment to changes of individual assignment costs. Conditioned on a sufficient level of robustness in relation to the size of the agents, we construct time-varying position bounds for every individual agent. These local constraints are a direct byproduct of the assignment procedure and only depend on the initial agent positions, the destinations that are to be visited, and a timing parameter. We prove that no agent that is assigned to move to one of the target locations collides with any other agent if all agents satisfy their local position constraints. We demonstrate the method in a illustrative case study.
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Tuning of multivariable model predictive controllers through expert bandit feedback

2020-02-18
Alex S. Ira , Chris Manzie , Iman Shames +4 more
For certain industrial control applications an explicit function capturing the non-trivial trade-off between competing objectives in closed loop performance is not available. In such scenarios it is common practice to … For certain industrial control applications an explicit function capturing the non-trivial trade-off between competing objectives in closed loop performance is not available. In such scenarios it is common practice to use the human innate ability to implicitly learn such a relationship and manually tune the corresponding controller to achieve the desirable closed loop performance. This approach has its deficiencies because of individual variations due to experience levels and preferences in the absence of an explicit calibration metric. Moreover, as the complexity of the underlying system and/or the controller increase, in the effort to achieve better performance, so does the tuning time and the associated tuning cost. To reduce the overall tuning cost, a tuning framework is proposed herein, whereby a supervised machine learning is used to extract the human-learned cost function and an optimisation algorithm that can efficiently deal with a large number of variables, is used for optimising the extracted cost function. Given the interest in the implementation across many industrial domains and the associated high degree of freedom present in the corresponding tuning process, a Model Predictive Controller applied to air path control in a diesel engine is tuned for the purpose of demonstrating the potential of the framework.
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Uncertainty Intervals for Robust Bottleneck Assignment

2019-06-01
Michael Elad , Tony A. Wood , Chris Manzie +1 more
We examine the robustness of bottleneck assignment problems to perturbations in the assignment weights. We derive two algorithms that provide uncertainty bounds for robust assignment. We prove that the bottleneck … We examine the robustness of bottleneck assignment problems to perturbations in the assignment weights. We derive two algorithms that provide uncertainty bounds for robust assignment. We prove that the bottleneck assignment is guaranteed to be invariant to perturbations which lie within the provided bounds. We apply the method to an example of task assignment for a multi-agent system.
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Sensitivity analysis in linear programming: just be careful!

1997-08-01
Benjamin Jansen , J.J. de Jong , C. Roos +1 more

Sensitivity analysis of the optimal assignment

2003-05-12
Chi-Jen Lin , Ue‐Pyng Wen

Robustness of exponential stability to singular perturbations and delays

2008-01-11
G. Grammel

A Distributed Version of the Hungarian Method for Multirobot Assignment

2017-05-22
Smriti Chopra , Giuseppe Notarstefano , Matthew Rice +1 more
In this paper, we propose a distributed version of the Hungarian method to solve the well-known assignment problem. In the context of multirobot applications, all robots cooperatively compute a common … In this paper, we propose a distributed version of the Hungarian method to solve the well-known assignment problem. In the context of multirobot applications, all robots cooperatively compute a common assignment that optimizes a given global criterion (e.g., the total distance traveled) within a finite set of local computations and communications over a peer-to-peer network. As a motivating application, we consider a class of multirobot routing problems with "spatiotemporal" constraints, i.e., spatial targets that require servicing at particular time instants. As a means of demonstrating the theory developed in this paper, the robots cooperatively find online suboptimal routes by applying an iterative version of the proposed algorithm in a distributed and dynamic setting. As a concrete experimental test bed, we provide an interactive "multirobot orchestral" framework, in which a team of robots cooperatively plays a piece of music on a so-called orchestral floor.
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Stability in the presence of singular perturbations

1998-12-01
Zvi Artstein

Tracking Fast Trajectories Along a Slow Dynamics: A Singular Perturbations Approach

1997-09-01
Zvi Artstein , Vladimir Gaitsgory
Controlled coupled slow and fast motions are examined in a singular perturbations setting. The objective is to minimize a cost functional that takes into account both the fast motion, supposing, … Controlled coupled slow and fast motions are examined in a singular perturbations setting. The objective is to minimize a cost functional that takes into account both the fast motion, supposing, say, tracking a fast target, and the slow dynamics. A method is offered to cope with the possibility that the fast flow has nonstationary limits. Invariant measures of the fast motion are then the controlled objects on the infinitesimal scale. Optimal amalgamation of them on the slow scale induces the variational limit, whose solutions are near optimal solutions of the perturbed system.

Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control

2014-06-10
Vladimir Gaitsgory , Sergey Rossomakhine
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High-dimensional semiparametric Gaussian copula graphical models

2012-08-01
Han Liu , Fang Han , Ming Yuan +2 more
We propose a semiparametric approach called the nonparanormal SKEPTIC for efficiently and robustly estimating high-dimensional undirected graphical models. To achieve modeling flexibility, we consider the nonparanormal graphical models proposed by … We propose a semiparametric approach called the nonparanormal SKEPTIC for efficiently and robustly estimating high-dimensional undirected graphical models. To achieve modeling flexibility, we consider the nonparanormal graphical models proposed by Liu, Lafferty and Wasserman [J. Mach. Learn. Res. 10 (2009) 2295–2328]. To achieve estimation robustness, we exploit nonparametric rank-based correlation coefficient estimators, including Spearman’s rho and Kendall’s tau. We prove that the nonparanormal SKEPTIC achieves the optimal parametric rates of convergence for both graph recovery and parameter estimation. This result suggests that the nonparanormal graphical models can be used as a safe replacement of the popular Gaussian graphical models, even when the data are truly Gaussian. Besides theoretical analysis, we also conduct thorough numerical simulations to compare the graph recovery performance of different estimators under both ideal and noisy settings. The proposed methods are then applied on a large-scale genomic data set to illustrate their empirical usefulness. The R package huge implementing the proposed methods is available on the Comprehensive R Archive Network: http://cran.r-project.org/.
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Analysis for a class of singularly perturbed hybrid systems via averaging

2012-03-30
Wei Wang , Andrew R. Teel , Dragan Nešić

Random Gradient-Free Minimization of Convex Functions

2015-11-30
Yurii Nesterov , Vladimir Spokoiny

Asymptotic stability of singularly perturbed differential equations

2016-11-03
Zvi Artstein

Averaging and Near Viability of Singularly Perturbed Control Systems

2006-01-01
Vladimir Gaitsgory , Mawson Lakes
In this paper we consider issues related to averaging of singularly perturbed control systems (SPCS) in the viability context. Despite of the fact that the averaging techniques for SPCS have … In this paper we consider issues related to averaging of singularly perturbed control systems (SPCS) in the viability context. Despite of the fact that the averaging techniques for SPCS have been studied very intensively (see [1]-[5], [8], [9], [13], [18], [19], [22], [23], [25], [29] for most recent developments and also for references to earlier results in the area), this topic, to the best of the author’s knowledge, has not been considered in the literature.

Averaging of singularly perturbed systems

1997-06-01
G. Grammel

Singularly perturbed differential inclusions: An averaging approach

1996-12-01
G. Grammel

Suboptimal control of singularly perturbed systems and periodic optimization

1993-06-01
Vladimir Gaitsgory
A traditional approach to singularly perturbed optimal control problems is based on an approximation of these problems by reduced problems which are obtained via the formal replacement of the fast … A traditional approach to singularly perturbed optimal control problems is based on an approximation of these problems by reduced problems which are obtained via the formal replacement of the fast variables by the states of equilibrium of the fast subsystems considered with frozen slow variables and controls. It is shown that such an approximation is valid if and only if certain families of periodic optimization problems admit steady state solutions. It is also shown how the solutions of these problems can be used to construct suboptimal controls for singularly perturbed problems when approximation by reduced problems is not possible.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A first course in order statistics

1993-04-01
Basic Distribution Theory Discrete Order Statistics Order Statistics from Some Specific Distributions Moment Relations, Bounds, and Approximations Characterizations Using Order Statistics Order Statistics in Statistical Inference Asymptotic Theory Record Values … Basic Distribution Theory Discrete Order Statistics Order Statistics from Some Specific Distributions Moment Relations, Bounds, and Approximations Characterizations Using Order Statistics Order Statistics in Statistical Inference Asymptotic Theory Record Values Bibliography Indexes.

Exploiting Structure in the Bottleneck Assignment Problem

2020-01-01
Mitchell Khoo , Tony A. Wood , Chris Manzie +1 more
An assignment problem arises when there exists a set of tasks that must be allocated to a set of agents. The bottleneck assignment problem (BAP) has the objective of minimising … An assignment problem arises when there exists a set of tasks that must be allocated to a set of agents. The bottleneck assignment problem (BAP) has the objective of minimising the most costly allocation of a task to an agent. Under certain conditions the structure of the BAP can be exploited such that subgroups of tasks are assigned separately with lower complexity and then merged to form a combined assignment. In particular, we discuss merging the assignments from two separate BAPs and use the solution of the subproblems to bound the solution of the combined problem. We also provide conditions for cases where the solution of the subproblems produces an exact solution to the BAP over the combined problem. We then introduce a particular algorithm for solving the BAP that takes advantage of this insight. The methods are demonstrated in a numerical case study.
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Personalized Online Adaptation of Kinematic Synergies for Human-Prosthesis Interfaces

2019-06-17
Ricardo Garcia-Rosas , Ying Tan , Denny Oetomo +2 more
Synergies have been adopted in prosthetic limb applications to reduce complexity of design, but typically involve a single synergy setting for a population and ignore individual preference or adaptation capacity. … Synergies have been adopted in prosthetic limb applications to reduce complexity of design, but typically involve a single synergy setting for a population and ignore individual preference or adaptation capacity. However, personalization of the synergy setting is necessary for the effective operation of the prosthetic device. Two major challenges hinder the personalization of synergies in human-prosthesis interfaces. The first is related to the process of human motor adaptation and the second to the variation in motor learning dynamics of individuals. In this paper, a systematic personalization of kinematic synergies for human-prosthesis interfaces using on-line measurements from each individual is proposed. The task of reaching using the upper-limb is described by an objective function and the interface is parameterized by a kinematic synergy. Consequently, personalizing the interface for a given individual can be formulated as finding an optimal personalized parameter. A structure to model the observed motor behavior that allows for the personalized traits of motor preference and motor learning is proposed, and subsequently used in an on-line optimization scheme to identify the synergies for an individual. The knowledge of the common features contained in the model enables on-line adaptation of the human-prosthesis interface to happen concurrently to human motor adaptation without the need to re-tune the personalization algorithm for each individual. Human-in-the-loop experimental results with able-bodied subjects, performed in a virtual reality environment to emulate amputation and prosthesis use, show that the proposed personalization algorithm was effective in obtaining optimal synergies with a fast uniform convergence speed across a group of individuals.
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CasADi: a software framework for nonlinear optimization and optimal control

2018-07-11
Joel A.E. Andersson , Joris Gillis , Greg Horn +2 more
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Real-Time Model Predictive Control for Energy Management in Autonomous Underwater Vehicle

2018-12-01
Niankai Yang , Mohammad Reza Amini , Matthew Johnson‐Roberson +1 more
Improving endurance is crucial for extending the spatial and temporal operation range of autonomous underwater vehicles (AUVs). Considering the hardware constraints and the performance requirements, an intelligent energy management system … Improving endurance is crucial for extending the spatial and temporal operation range of autonomous underwater vehicles (AUVs). Considering the hardware constraints and the performance requirements, an intelligent energy management system is required to extend the operation range of AUVs. This paper presents a novel model predictive control (MPC) framework for energy-optimal point-to-point motion control of an AUV. In this scheme, the energy management problem of an AUV is reformulated as a surge motion optimization problem in two stages. First, a system-level energy minimization problem is solved by managing the trade-off between the energies required for overcoming the positive buoyancy and surge drag force in static optimization. Next, an MPC with a special cost function formulation is proposed to deal with transients and system dynamics. A switching logic for handling the transition between the static and dynamic stages is incorporated to reduce the computational efforts. Simulation results show that the proposed method is able to achieve near-optimal energy consumption with considerable lower computational complexity.
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Online Optimization Using Zeroth Order Oracles

2019-06-07
Iman Shames , Daniel Selvaratnam , Jonathan H. Manton
This letter considers the iterative numerical optimization of time-varying cost functions where no gradient information is available at each iteration. In this case, the proposed algorithm estimates a directional derivative … This letter considers the iterative numerical optimization of time-varying cost functions where no gradient information is available at each iteration. In this case, the proposed algorithm estimates a directional derivative by finite differences. The main contributions are the derivation of error bounds for such algorithms and proposal of optimal algorithm parameter values, e.g., step-sizes, for strongly convex cost functions. The algorithm is applied to tackle a source localization problem using a sensing agent where the source actively evades the agent. Numerical examples are provided to illustrate the theoretical results.

Model predictive controller with average emissions constraints for diesel airpath

2019-07-11
Gokul S. Sankar , Rohan C. Shekhar , Chris Manzie +2 more
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Grasp Constraint Satisfaction for Object Manipulation using Robotic Hands

2018-12-01
Wenceslao Shaw Cortez , Denny Oetomo , Chris Manzie +1 more
For successful object manipulation with robotic hands, it is important to ensure that the object remains in the grasp at all times. In addition to grasp constraints associated with slipping … For successful object manipulation with robotic hands, it is important to ensure that the object remains in the grasp at all times. In addition to grasp constraints associated with slipping and singular hand configurations, excessive rolling is an important grasp concern where the contact points roll off of the fingertip surface. Related literature focus only on a subset of grasp constraints, or assume grasp constraint satisfaction without providing guarantees of such a claim. In this paper, we propose a control approach that systematically handles all grasp constraints. The proposed controller ensures that the object does not slip, joints do not exceed joint angle constraints (e.g. reach singular configurations), and the contact points remain in the fingertip workspace. The proposed controller accepts a nominal manipulation control, and ensures the grasping constraints are satisfied to support the assumptions made in the literature. Simulation results validate the proposed approach.
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A quasi-newton differential dynamic programming algorithm for discrete-time optimal control

1987-11-01
Suvrajeet Sen , S. Yakowitz

Lipschitz constants in experimental optimization

2016-01-01
Gene A. Bunin , Grégory François
The Lipschitz constant of a response surface function upper bounds the sensitivity of a dependent variable to changes in the independent ones. Traditionally, such constants have found much implicit and … The Lipschitz constant of a response surface function upper bounds the sensitivity of a dependent variable to changes in the independent ones. Traditionally, such constants have found much implicit and abstract use in mathematically oriented applications, but their potential for explicit use in more engineering-based domains has not been explored. The latter point is the subject of this paper, where we propose several ways in which the Lipschitz constants may be used explicitly in the domain of experimental optimization. Specifically, we focus on how they may help ensure the satisfaction of constraints and on their potential role in reducing the negative effects of measurement or estimation uncertainty. A number of refinements to the proposed approaches are also derived, and some techniques for setting the constants are presented.
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Global Optimality in Low-Rank Matrix Optimization

2018-05-10
Zhihui Zhu , Qiuwei Li , Gongguo Tang +1 more
This paper considers the minimization of a general objective function $f(X)$ over the set of rectangular $n\times m$ matrices that have rank at most $r$. To reduce the computational burden, … This paper considers the minimization of a general objective function $f(X)$ over the set of rectangular $n\times m$ matrices that have rank at most $r$. To reduce the computational burden, we factorize the variable $X$ into a product of two smaller matrices and optimize over these two matrices instead of $X$. Despite the resulting nonconvexity, recent studies in matrix completion and sensing have shown that the factored problem has no spurious local minima and obeys the so-called strict saddle property (the function has a directional negative curvature at all critical points but local minima). We analyze the global geometry for a general and yet well-conditioned objective function $f(X)$ whose restricted strong convexity and restricted strong smoothness constants are comparable. In particular, we show that the reformulated objective function has no spurious local minima and obeys the strict saddle property. These geometric properties imply that a number of iterative optimization algorithms (such as gradient descent) can provably solve the factored problem with global convergence.
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Introduction to Online Convex Optimization

2016-01-01
Elad Hazan
Introduction to Online Convex Optimization portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model … Introduction to Online Convex Optimization portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization. It is necessary as well as beneficial to take a robust approach, by applying an optimization method that learns as one goes along, learning from experience as more aspects of the problem are observed. This view of optimization as a process has become prominent in varied fields and has led to some spectacular success in modeling and systems that are now part of our daily lives. Introduction to Online Convex Optimization is intended to serve as a reference for a self-contained course on online convex optimization and the convex optimization approach to machine learning for the educated graduate student in computer science/electrical engineering/ operations research/statistics and related fields. It is also an ideal reference for the researcher diving into this fascinating world at the intersection of optimization and machine learning.
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Distributed Stochastic Optimization via Matrix Exponential Learning

2017-01-23
Panayotis Mertikopoulos , E. Veronica Belmega , Romain Negrel +1 more
In this paper, we investigate a distributed learning scheme for a broad class of stochastic optimization problems and games that arise in signal processing and wireless communications. The proposed algorithm … In this paper, we investigate a distributed learning scheme for a broad class of stochastic optimization problems and games that arise in signal processing and wireless communications. The proposed algorithm relies on the method of matrix exponential learning (MXL) and only requires locally computable gradient observations that are possibly imperfect and/or obsolete. To analyze it, we introduce the notion of a stable Nash equilibrium and we show that the algorithm is globally convergent to such equilibria - or locally convergent when an equilibrium is only locally stable. We also derive an explicit linear bound for the algorithm's convergence speed, which remains valid under measurement errors and uncertainty of arbitrarily high variance. To validate our theoretical analysis, we test the algorithm in realistic multi-carrier/multiple-antenna wireless scenarios where several users seek to maximize their energy efficiency. Our results show that learning allows users to attain a net increase between 100% and 500% in energy efficiency, even under very high uncertainty.
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Robustness of Control Barrier Functions for Safety Critical Control

2015-01-01
Xiangru Xu , Paulo Tabuada , Jessy W. Grizzle +1 more
Abstract Barrier functions (also called certificates) have been an important tool for the verification of hybrid systems, and have also played important roles in optimization and multi-objective control. The extension … Abstract Barrier functions (also called certificates) have been an important tool for the verification of hybrid systems, and have also played important roles in optimization and multi-objective control. The extension of a barrier function to a controlled system results in a control barrier function. This can be thought of as being analogous to how Sontag extended Lyapunov functions to control Lypaunov functions in order to enable controller synthesis for stabilization tasks. A control barrier function enables controller synthesis for safety requirements specified by forward invariance of a set using a Lyapunov-like condition. This paper develops several important extensions to the notion of a control barrier function. The first involves robustness under perturbations to the vector field defining the system. Input-to-State stability conditions are given that provide for forward invariance, when disturbances are present, of a “relaxation” of set rendered invariant without disturbances. A control barrier function can be combined with a control Lyapunov function in a quadratic program to achieve a control objective subject to safety guarantees. The second result of the paper gives conditions for the control law obtained by solving the quadratic program to be Lipschitz continuous and therefore to gives rise to well-defined solutions of the resulting closed-loop system.
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Online Learning With Inexact Proximal Online Gradient Descent Algorithms

2019-01-01
Rishabh Dixit , Amrit Singh Bedi , Ruchi Tripathi +1 more
We consider non-differentiable dynamic optimization problems such as those arising in robotics and subspace tracking. Given the computational constraints and the time-varying nature of the problem, a low-complexity algorithm is … We consider non-differentiable dynamic optimization problems such as those arising in robotics and subspace tracking. Given the computational constraints and the time-varying nature of the problem, a low-complexity algorithm is desirable, while the accuracy of the solution may only increase slowly over time. We put forth the proximal online gradient descent (OGD) algorithm for tracking the optimum of a composite objective function comprising of a differentiable loss function and a non-differentiable regularizer. An online learning framework is considered and the gradient of the loss function is allowed to be erroneous. Both, the gradient error as well as the dynamics of the function optimum or target are adversarial and the performance of the inexact proximal OGD is characterized in terms of its dynamic regret, expressed in terms of the cumulative error and path length of the target. The proposed inexact proximal OGD is generalized for application to large-scale problems where the loss function has a finite sum structure. In such cases, evaluation of the full gradient may not be viable and a variance reduced version is proposed that allows the component functions to be sub-sampled. The efficacy of the proposed algorithms is tested on the problem of formation control in robotics and on the dynamic foreground-background separation problem in video.
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Distributed Model Predictive Control for Linear Systems With Adaptive Terminal Sets

2019-05-14
Georgios Darivianakis , Annika Eichler , John Lygeros
We propose a distributed model predictive control scheme for linear time-invariant constrained systems that admit a separable structure. To exploit the merits of distributed computation algorithms, the terminal cost and … We propose a distributed model predictive control scheme for linear time-invariant constrained systems that admit a separable structure. To exploit the merits of distributed computation algorithms, the terminal cost and invariant terminal set of the optimal control problem need to respect the coupling structure of the system. Existing methods to address this issue typically separate the synthesis of terminal controllers and costs from the one of terminal sets, and do not explicitly consider the effect of the current and predicted system states on this synthesis process. These limitations can adversely affect performance due to small or even empty terminal sets. Here, we present a unified framework to encapsulate the synthesis of both the stabilizing terminal controller and invariant terminal set into the same optimization problem. Conditions for Lyapunov stability and invariance are imposed in the synthesis problem in a way that allows the terminal cost and invariant terminal set to admit the desired distributed structure. We illustrate the effectiveness of the proposed method on several numerical examples.
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On Feasibility, Stability and Performance in Distributed Model Predictive Control

2014-03-20
Pontus Giselsson , Anders Rantzer
In distributed model predictive control (DMPC), where a centralized optimization problem is solved in distributed fashion using dual decomposition, it is important to keep the number of iterations in the … In distributed model predictive control (DMPC), where a centralized optimization problem is solved in distributed fashion using dual decomposition, it is important to keep the number of iterations in the solution algorithm small. In this technical note, we present a stopping condition to such distributed solution algorithms that is based on a novel adaptive constraint tightening approach. The stopping condition guarantees feasibility of the optimization problem and stability and a prespecified performance of the closed-loop system.
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Nonlinear programming without a penalty function

2002-01-01
R. Fletcher , Sven Leyffer

On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming

2005-04-28
Andreas Wächter , Lorenz T. Biegler

First-order methods of smooth convex optimization with inexact oracle

2013-06-13
Olivier Devolder , François Glineur , Yurii Nesterov

Generalized equations and their solutions, part II: Applications to nonlinear programming

1982-01-01
Stephen M. Robinson

A convexifying algorithm for the design of structured linear controllers

2002-11-11
Maurı́cio C. de Oliveira , Juan F. Camino , Robert E. Skelton
Addresses the design of linear controllers with special structure imposed on the gain matrix. This problem is called a SLC (structured linear control) problem. The SLC problem includes fixed order … Addresses the design of linear controllers with special structure imposed on the gain matrix. This problem is called a SLC (structured linear control) problem. The SLC problem includes fixed order output feedback control, decentralized control, joint plant and control design, and many other linear control problems. A theoretical framework that allows one to pursue the solution of SLC problems is provided. Although the obtained conditions are nonconvex, it is shown that solving a SLC problem involving standard control objectives such as stability, bounds on the H/sub 2/ or H/sub /spl infin// norms, and real positiveness is not harder than solving a standard unstructured static output feedback problem. A convexifying algorithm that might be used to solve the SLC problem is also developed. At each iteration a certain function is added to the constraints in order to make them convex. At convergence, the artificially introduced convexifying functions reduce to zero, guaranteeing the feasibility of the original problem. Local optimality can be guaranteed. Some examples illustrate how the SLC framework and the convexifying algorithm can improve the solutions of control problem with suboptimal solutions available.

Local Convergence of Sequential Convex Programming for Nonconvex Optimization

2010-01-01
Quoc Tran Dinh , Moritz Diehl

On the formulation and theory of the Newton interior-point method for nonlinear programming

1996-06-01
Amr El-Bakry , R. A. Tapia , Takashi Tsuchiya +1 more

Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems

2012-01-01
Sébastien Bubeck , Nicolò Cesa‐Bianchi
A multi-armed bandit problem - or, simply, a bandit problem - is a sequential allocation problem defined by a set of actions. At each time step, a unit resource is … A multi-armed bandit problem - or, simply, a bandit problem - is a sequential allocation problem defined by a set of actions. At each time step, a unit resource is allocated to an action and some observable payoff is obtained. The goal is to maximize the total payoff obtained in a sequence of allocations. The name bandit refers to the colloquial term for a slot machine (a "one-armed bandit" in American slang). In a casino, a sequential allocation problem is obtained when the player is facing many slot machines at once (a "multi-armed bandit"), and must repeatedly choose where to insert the next coin. Multi-armed bandit problems are the most basic examples of sequential decision problems with an exploration-exploitation trade-off. This is the balance between staying with the option that gave highest payoffs in the past and exploring new options that might give higher payoffs in the future. Although the study of bandit problems dates back to the 1930s, exploration-exploitation trade-offs arise in several modern applications, such as ad placement, website optimization, and packet routing. Mathematically, a multi-armed bandit is defined by the payoff process associated with each option. In this book, the focus is on two extreme cases in which the analysis of regret is particularly simple and elegant: independent and identically distributed payoffs and adversarial payoffs. Besides the basic setting of finitely many actions, it also analyzes some of the most important variants and extensions, such as the contextual bandit model. This monograph is an ideal reference for students and researchers with an interest in bandit problems.
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Why a Pure Primal Newton Barrier Step May be Infeasible

1995-02-01
Margaret H. Wright
Modern barrier methods for constrained optimization are sometimes portrayed conceptually as a sequence of inexact minimizations, with only a very few Newton iterations (perhaps just one) for each value of … Modern barrier methods for constrained optimization are sometimes portrayed conceptually as a sequence of inexact minimizations, with only a very few Newton iterations (perhaps just one) for each value of the barrier parameter. Unfortunately, this rosy image does not accurately reflect reality when the barrier parameter is reduced at a reasonable rate, as in a practical (long-step) method. Local analysis is presented indicating why a pure Newton step in a typical long-step barrier method for nonlinearly constrained optimization may be seriously infeasible, even when taken from an apparently favorable point; hence accurate calculation of the Newton direction does not guarantee an effective algorithm. The features described are illustrated numerically and connected to known theoretical results for well-behaved convex problems satisfying common assumptions such as self-concordancy. The contrasting nature of an approximate step to the desired minimizes of the barrier function is also discussed.

Input‐to‐state stability, numerical dynamics and sampled‐data control

2008-02-29
Lars Grüne
Abstract We investigate the relation between asymptotic stability for dynamical systems and families of approximations. Using suitably perturbed systems and the input‐to‐state stability property we develop a framework which yields … Abstract We investigate the relation between asymptotic stability for dynamical systems and families of approximations. Using suitably perturbed systems and the input‐to‐state stability property we develop a framework which yields necessary and sufficient conditions on the stability of the approximations ensuring stability of the approximated system. The results are formulated for numerical one step schemes for ordinary differential equations and for sampled‐data systems. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

A proof of asymptotic normality for some VARX models

1995-12-01
Mohamed Boutahar , Claude Deniau

Quantization Design for Distributed Optimization

2016-08-16
Ye Pu , Melanie N. Zeilinger , Colin N. Jones
We consider the problem of solving a distributed optimization problem using a distributed computing platform, where the communication in the network is limited: each node can only communicate with its … We consider the problem of solving a distributed optimization problem using a distributed computing platform, where the communication in the network is limited: each node can only communicate with its neighbors and the channel has a limited data-rate. A common technique to address the latter limitation is to apply quantization to the exchanged information. We propose two distributed optimization algorithms with an iteratively refining quantization design based on the inexact proximal gradient method and its accelerated variant. We show that if the parameters of the quantizers, i.e., the number of bits and the initial quantization intervals, satisfy certain conditions, then the quantization error is bounded by a linearly decreasing function and the convergence of the distributed algorithms is guaranteed. Furthermore, we prove that after imposing the quantization scheme, the distributed algorithms still exhibit a linear convergence rate, and show complexity upper-bounds on the number of iterations to achieve a given accuracy. Finally, we demonstrate the performance of the proposed algorithms and the theoretical findings for solving a distributed optimal control problem.
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