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Minimizing Pumping Energy Cost in Real-Time Operations of Water Distribution Systems Using Economic Model Predictive Control

Authors

Ye Wang, Kevin Too Yok, Wenyan Wu, Angus R. Simpson, Erik Weyer, Chris Manzie
Type: Article
Publication Date: 2021-05-13
Citations: 22
DOI: https://doi.org/10.1061/(asce)wr.1943-5452.0001399

Abstract

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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  • Journal of Water Resources Planning and Management
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  • arXiv (Cornell University)
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Economic Model Predictive Control of Water Distribution Systems with Accelerated Optimization Algorithm

2024-06-10
Saskia A. Putri , Faegheh Moazeni , Javad Khazaei
Model predictive control (MPC) has emerged as an effective strategy for water distribution systems (WDSs) management. However, it is hampered by the computational burden for large-scale WDSs due to the … Model predictive control (MPC) has emerged as an effective strategy for water distribution systems (WDSs) management. However, it is hampered by the computational burden for large-scale WDSs due to the combinatorial growth of possible control actions that must be evaluated at each time step. Therefore, a fast computation algorithm to implement MPC in WDSs can be obtained using a move-blocking approach that simplifies control decisions while ensuring solution feasibility. This paper introduces a least-restrictive move-blocking that interpolates the blocked control rate of change, aiming at balancing computational efficiency with operational effectiveness. The proposed control strategy is demonstrated on aggregated WDSs, encompassing multiple hydraulic elements. This implementation is incorporated into a multi-objective optimization framework that concurrently optimizes water level security of the storage tanks, smoothness of the control actions, and cost-effective objectives. A fair comparison between the proposed approach with the non-blocking Economic MPC is provided.
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Economic Predictive Control with Periodic Horizon for Water Distribution Networks

2023-01-01
Mirhan Ürkmez , Carsten Skovmose Kallesøe , Jan Dimon Bendtsen +1 more
This paper deals with control of pumps in large-scale water distribution networks with the aim of minimizing economic costs while satisfying operational constraints. Finding a control algorithm in combination with … This paper deals with control of pumps in large-scale water distribution networks with the aim of minimizing economic costs while satisfying operational constraints. Finding a control algorithm in combination with a model that can be applied in real-time is a challenging problem due to the nonlinearities presented by the pipes and the network sizes. We propose a predictive control algorithm with a periodic horizon. The method provides a way for the economic operation of large water networks with a low-complexity linear model. Economic Predictive control with a periodic horizon and a terminal state constraint is constructed to keep the state trajectories close to an optimal periodic trajectory. Barrier terms are also included in the cost function to prevent constraint violations. The proposed method is tested on a state-of-the-art EPANET model of the water network of a medium size Danish town (Randers) and shown to perform as intended under varying conditions.
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Economic Predictive Control with Periodic Horizon for Water Distribution Networks

2023-01-01
Mirhan Ürkmez , Carsten Skovmose Kallesøe , Jan Dimon Bendtsen +1 more
This paper deals with the control of pumps in large-scale water distribution networks with the aim of minimizing economic costs while satisfying operational constraints. Finding a control algorithm in combination … This paper deals with the control of pumps in large-scale water distribution networks with the aim of minimizing economic costs while satisfying operational constraints. Finding a control algorithm in combination with a model that can be applied in real-time is a challenging problem due to the nonlinearities presented by the pipes and the network sizes. We propose a predictive control algorithm with a periodic horizon. The method provides a way for the economic operation of large water networks with a small linear model. Economic Predictive control with a periodic horizon and a terminal state constraint is constructed to keep the state trajectories close to an optimal periodic trajectory. Barrier terms are also included in the cost function to prevent constraint violations. The proposed method is tested on the EPANET implementation of the water network of a medium size Danish town (Randers) and shown to perform as intended under varying conditions.
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Hybrid Reinforcement Learning for Optimizing Pump Sustainability in Real-World Water Distribution Networks

2023-01-01
Harsh Patel , Yuan Zhou , Alexander P Lamb +2 more
This article addresses the pump-scheduling optimization problem to enhance real-time control of real-world water distribution networks (WDNs). Our primary objectives are to adhere to physical operational constraints while reducing energy … This article addresses the pump-scheduling optimization problem to enhance real-time control of real-world water distribution networks (WDNs). Our primary objectives are to adhere to physical operational constraints while reducing energy consumption and operational costs. Traditional optimization techniques, such as evolution-based and genetic algorithms, often fall short due to their lack of convergence guarantees. Conversely, reinforcement learning (RL) stands out for its adaptability to uncertainties and reduced inference time, enabling real-time responsiveness. However, the effective implementation of RL is contingent on building accurate simulation models for WDNs, and prior applications have been limited by errors in simulation training data. These errors can potentially cause the RL agent to learn misleading patterns and actions and recommend suboptimal operational strategies. To overcome these challenges, we present an improved "hybrid RL" methodology. This method integrates the benefits of RL while anchoring it in historical data, which serves as a baseline to incrementally introduce optimal control recommendations. By leveraging operational data as a foundation for the agent's actions, we enhance the explainability of the agent's actions, foster more robust recommendations, and minimize error. Our findings demonstrate that the hybrid RL agent can significantly improve sustainability, operational efficiency, and dynamically adapt to emerging scenarios in real-world WDNs.
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Polyhedral Relaxations for Optimal Pump Scheduling of Potable Water Distribution Networks

2022-01-01
Byron Tasseff , Russell Bent , Carleton Coffrin +6 more
The classic pump scheduling or Optimal Water Flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. … The classic pump scheduling or Optimal Water Flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over forty-five literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods.
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Deep Reinforcement Learning for Real-Time Optimization of Pumps in Water Distribution Systems

2020-08-25
Gergely Hajgató , György Paál , Bálint Gyires-Tóth
Real-time control of pumps can be an infeasible task in water distribution systems (WDSs) because the calculation to find the optimal pump speeds is resource-intensive. The computational need cannot be … Real-time control of pumps can be an infeasible task in water distribution systems (WDSs) because the calculation to find the optimal pump speeds is resource-intensive. The computational need cannot be lowered even with the capabilities of smart water networks when conventional optimization techniques are used. Deep reinforcement learning (DRL) is presented here as a controller of pumps in two WDSs. An agent based on a dueling deep q-network is trained to maintain the pump speeds based on instantaneous nodal pressure data. General optimization techniques (e.g., Nelder-Mead method, differential evolution) serve as baselines. The total efficiency achieved by the DRL agent compared to the best performing baseline is above 0.98, whereas the speedup is around 2x compared to that. The main contribution of the presented approach is that the agent can run the pumps in real-time because it depends only on measurement data. If the WDS is replaced with a hydraulic simulation, the agent still outperforms conventional techniques in search speed.
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Uncertainty-Aware Methods for Leveraging Water Pumping Flexibility for Power Networks

2022-01-01
Anna Stuhlmacher , Johanna L. Mathieu
Recent work has demonstrated that water supply pumps in the drinking water distribution network can be leveraged to provide flexibility to the power network, but existing approaches are computationally demanding … Recent work has demonstrated that water supply pumps in the drinking water distribution network can be leveraged to provide flexibility to the power network, but existing approaches are computationally demanding and/or overly conservative. In this paper, we develop a computationally tractable probabilistic approach to schedule and control water pumping to provide voltage support to the power distribution network subject to power and water distribution network constraints under power demand uncertainty. Building upon robust and chance-constrained reformulation approaches, we analytically reformulate the probabilistic problem into a deterministic one and solve for the scheduled pump operation and the control policy parameters that adjust the pumps based on the power demand forecast error realizations. In a case study, we compare our proposed approach to an adjustable robust method and investigate the performance in terms of computation time, cost, and empirical violation probabilities. We find that our proposed approach is computationally tractable and is less conservative than the robust approach, indicating that our formulation would be scalable to larger networks.
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Nested Algorithms for Optimal Reservoir Operation and Their Embedding in a Decision Support Platform

2020-04-30
Blagoj Delipetrev
Reservoir operation is a multi-objective optimization problem, and is traditionally solved with dynamic programming (DP) and stochastic dynamic programming (SDP) algorithms. The thesis presents novel algorithms for optimal reservoir operation, … Reservoir operation is a multi-objective optimization problem, and is traditionally solved with dynamic programming (DP) and stochastic dynamic programming (SDP) algorithms. The thesis presents novel algorithms for optimal reservoir operation, named nested DP (nDP), nested SDP (nSDP), nested reinforcement learning (nRL) and their multi-objective (MO) variants, correspondingly MOnDP, MOnSDP and MOnRL. The idea is to include a nested optimization algorithm into each state transition, which reduces the initial problem dimension and alleviates the curse of dimensionality. These algorithms can solve multi-objective optimization problems, without significantly increasing the algorithm complexity or the computational expenses. It can additionally handle dense and irregular variable discretization. All algorithms are coded in Java and were tested on the case study of the Knezevo reservoir in the Republic of Macedonia. Nested optimization algorithms are embedded in a cloud application platform for water resources modeling and optimization. The platform is available 24/7, accessible from everywhere, scalable, distributed, interoperable, and it creates a real-time multiuser collaboration platform.This thesis contributes with new and more powerful algorithms for an optimal reservoir operation and cloud application platform. All source codes are available for public use and can be used by researchers and practitioners to further advance the mentioned areas.
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Renewable Energy Supply Mode-Based Multi-Objective Daily Optimal Control of Cascade Pumping Stations with High-Frequency Data

2025-01-01
Luyan Zhou , Guangtao Fu , Hanyuan Li +4 more

Receding Horizon Control for Drinking Water Networks: The Case for Geometric Programming

2020-01-07
Shen Wang , Ahmad F. Taha , Nikolaos Gatsis +1 more
Optimal, network-driven control of water distribution networks (WDNs) is very difficult: valve and pump models form nontrivial, combinatorial logic; hydraulic models are nonconvex; water demand patterns are uncertain; and WDNs … Optimal, network-driven control of water distribution networks (WDNs) is very difficult: valve and pump models form nontrivial, combinatorial logic; hydraulic models are nonconvex; water demand patterns are uncertain; and WDNs are naturally of large scale. Prior research on control of WDN addressed major research challenges, yet either i) adopted simplified hydraulic models, WDN topologies, and rudimentary valve/pump modeling or ii) used mixed-integer, nonconvex optimization to solve WDN control problems. The objective of this article is to develop tractable computational algorithms to manage WDN operation, while considering arbitrary topology, flow direction, an abundance of valve types, control objectives, hydraulic models, and operational constraints-all while only using convex, continuous optimization. Specifically, we propose new geometric programming (GP)-based model predictive control (MPC) algorithms, designed to solve the water flow equations and obtain WDN controls, i.e., pump/valve schedules alongside heads and flows. The proposed approach amounts to solving a series of convex optimization problems that graciously scale to large networks. The proposed approach is tested using a 126-node network with many valves and pumps and is shown to outperform traditional, rule-based control. The developed GP-based MPC algorithms, as well as the numerical test results, are all included on Github.
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Optimal Scheduling of Variable Speed Pumps Using Mixed Integer Linear Programming -- Towards An Automated Approach

2023-01-01
Tomasz Janus , Bogumił Ulanicki , Kegong Diao
This article describes the methodology for formulating and solving optimal pump scheduling problems with variable-speed pumps (VSPs) as mixed integer linear programs (MILPs) using piece-linear approximations of the network components. … This article describes the methodology for formulating and solving optimal pump scheduling problems with variable-speed pumps (VSPs) as mixed integer linear programs (MILPs) using piece-linear approximations of the network components. The water distribution network (WDN) is simulated with an initial pump schedule for a defined time horizon, e.g. 24 hours, using a nonlinear algebraic solver. Next, the network element equations including VSPs are approximated with linear and piece-linear functions around chosen operating point(s). Finally, a fully parameterized MILP is formulated in which the objective is the total pumping cost. The method was used to solve a pump scheduling problem on a a simple two variable speed pump single-tank network that allows the reader to easily understand how the methodology works and how it is applied in practice. The obtained results showed that the formulation is robust and the optimizer is able to return global optimal result in a reliable manner for a range of operating points.
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Optimal management of pumped hydroelectric production with state constrained optimal control

2020-06-10
Athena Picarelli , Tiziano Vargiolu
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Real-Time Pumping Optimization of Combined Sewer Overflow Systems

2025-05-15
Yui‐Lam Chan , R. Dziedzic , Gal Perelman +1 more

Receding Horizon Control for Drinking Water Networks: The Case for Geometric Programming

2019-01-01
Shen Wang , Ahmad F. Taha , Nikolaos Gatsis +1 more
Optimal, network-driven control of Water Distribution Networks (WDN) is very difficult: valve and pump models form non-trivial, combinatorial logic; hydraulic models are nonconvex; water demand patterns are uncertain; and WDN … Optimal, network-driven control of Water Distribution Networks (WDN) is very difficult: valve and pump models form non-trivial, combinatorial logic; hydraulic models are nonconvex; water demand patterns are uncertain; and WDN are naturally large-scale. Prior research on control of WDN addressed major research challenges, yet either (i) adopted simplified hydraulic models, WDN topologies, and rudimentary valve/pump modeling or (ii) used mixed-integer, nonconvex optimization to solve WDN control problems. The objective of this paper is to develop tractable computational algorithms to manage WDN operation, while considering arbitrary topology, flow direction, an abundance of valve types, control objectives, hydraulic models, and operational constraints---all while only using convex, continuous optimization. Specifically, we propose new Geometric Programming (GP)-based Model Predictive Control (MPC) algorithms, designed to solve the water flow equations and obtain WDN controls, i.e., pump/valve schedules alongside heads and flows. The proposed approach amounts to solving a series of convex optimization problems that graciously scale to large networks. The proposed approach is tested using a 126-node network with many valves and pumps and shown to outperform traditional, rule-based control. The developed GP-based MPC algorithms, as well as the numerical test results are all included on Github.
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Polyhedral Relaxations for Optimal Pump Scheduling of Potable Water Distribution Networks

2024-02-15
Byron Tasseff , Russell Bent , Carleton Coffrin +6 more
The classic pump scheduling or optimal water flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. … The classic pump scheduling or optimal water flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over 45 literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Applications. Funding: This work was supported by the U.S. Department of Energy (DOE) Advanced Grid Modeling project, Coordinated Planning and Operation of Water and Power Infrastructures for Increased Resilience and Reliability. Incorporation of the PolyhedralRelaxations Julia package was supported by Los Alamos National Laboratory’s Directed Research and Development program under the project Fast, Linear Programming-Based Algorithms with Solution Quality Guarantees for Nonlinear Optimal Control Problems [Grant 20220006ER]. All work at Los Alamos National Laboratory was conducted under the auspices of the National Nuclear Security Administration of the U.S. DOE, Contract No. 89233218CNA000001. This work was also authored in part by the National Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, LLC, for the U.S. DOE, Contract No. DE-AC36-08GO28308. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0233 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0233 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .
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Uncertainty-aware demand management of water distribution networks in deregulated energy markets

2017-12-14
Pantelis Sopasakis , Ajay Kumar Sampathirao , Alberto Bemporad +1 more
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Hardware-in-the-Loop Simulation of Data-Driven Economic Dispatch Problem for Integrated Water–Energy Systems

2025-05-15
Oluwabunmi M. Iwakin , Faegheh Moazeni

Learning Optimal Control of Water Distribution Networks Through Sequential Model-Based Optimization

2020-01-01
Antonio Candelieri , Bruno G. Galuzzi , Ilaria Giordani +1 more
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Optimal Scheduling of Water Distribution Systems

2018-06-20
Manish K. Singh , Vassilis Kekatos
With dynamic electricity pricing, the operation of water distribution systems (WDS) is expected to become more variable. The pumps moving water from reservoirs to tanks and consumers, can serve as … With dynamic electricity pricing, the operation of water distribution systems (WDS) is expected to become more variable. The pumps moving water from reservoirs to tanks and consumers, can serve as energy storage alternatives if properly operated. Nevertheless, optimal WDS scheduling is challenged by the hydraulic law, according to which the pressure along a pipe drops proportionally to its squared water flow. The optimal water flow (OWF) task is formulated here as a mixed-integer non-convex problem incorporating flow and pressure constraints, critical for the operation of fixed-speed pumps, tanks, reservoirs, and pipes. The hydraulic constraints of the OWF problem are subsequently relaxed to second-order cone constraints. To restore feasibility of the original non-convex constraints, a penalty term is appended to the objective of the relaxed OWF. The modified problem can be solved as a mixed-integer second-order cone program, which is analytically shown to yield WDS-feasible minimizers under certain sufficient conditions. Under these conditions, by suitably weighting the penalty term, the minimizers of the relaxed problem can attain arbitrarily small optimality gaps, thus providing OWF solutions. Numerical tests using real-world demands and prices on benchmark WDS demonstrate the relaxation to be exact even for setups where the sufficient conditions are not met.
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Optimal Scheduling of Water Distribution Systems

2018-01-01
Manish Kumar Singh , Vassilis Kekatos
With dynamic electricity pricing, the operation of water distribution systems (WDS) is expected to become more variable. The pumps moving water from reservoirs to tanks and consumers, can serve as … With dynamic electricity pricing, the operation of water distribution systems (WDS) is expected to become more variable. The pumps moving water from reservoirs to tanks and consumers, can serve as energy storage alternatives if properly operated. Nevertheless, optimal WDS scheduling is challenged by the hydraulic law, according to which the pressure along a pipe drops proportionally to its squared water flow. The optimal water flow (OWF) task is formulated here as a mixed-integer non-convex problem incorporating flow and pressure constraints, critical for the operation of fixed-speed pumps, tanks, reservoirs, and pipes. The hydraulic constraints of the OWF problem are subsequently relaxed to second-order cone constraints. To restore feasibility of the original non-convex constraints, a penalty term is appended to the objective of the relaxed OWF. The modified problem can be solved as a mixed-integer second-order cone program, which is analytically shown to yield WDS-feasible minimizers under certain sufficient conditions. Under these conditions, by suitably weighting the penalty term, the minimizers of the relaxed problem can attain arbitrarily small optimality gaps, thus providing OWF solutions. Numerical tests using real-world demands and prices on benchmark WDS demonstrate the relaxation to be exact even for setups where the sufficient conditions are not met.
Chat View PDF

Economic Predictive Control with Periodic Horizon for Water Distribution Networks

2023-01-01
Mirhan Ürkmez , Carsten Skovmose Kallesøe , Jan Dimon Bendtsen +1 more
This paper deals with control of pumps in large-scale water distribution networks with the aim of minimizing economic costs while satisfying operational constraints. Finding a control algorithm in combination with … This paper deals with control of pumps in large-scale water distribution networks with the aim of minimizing economic costs while satisfying operational constraints. Finding a control algorithm in combination with a model that can be applied in real-time is a challenging problem due to the nonlinearities presented by the pipes and the network sizes. We propose a predictive control algorithm with a periodic horizon. The method provides a way for the economic operation of large water networks with a low-complexity linear model. Economic Predictive control with a periodic horizon and a terminal state constraint is constructed to keep the state trajectories close to an optimal periodic trajectory. Barrier terms are also included in the cost function to prevent constraint violations. The proposed method is tested on a state-of-the-art EPANET model of the water network of a medium size Danish town (Randers) and shown to perform as intended under varying conditions.
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Distributed economic predictive control of integrated energy systems for enhanced synergy and grid response: A decomposition and cooperation strategy

2023-07-27
Long Wu , Xunyuan Yin , Lei Pan +1 more
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YALMIP : a toolbox for modeling and optimization in MATLAB

2005-03-21
Johan Löfberg
The MATLAB toolbox YALMIP is introduced. It is described how YALMIP can be used to model and solve optimization problems typically occurring in systems and control theory. In this paper, … The MATLAB toolbox YALMIP is introduced. It is described how YALMIP can be used to model and solve optimization problems typically occurring in systems and control theory. In this paper, free MATLAB toolbox YALMIP, developed initially to model SDPs and solve these by interfacing eternal solvers. The toolbox makes development of optimization problems in general, and control oriented SDP problems in particular, extremely simple. In fact, learning 3 YALMIP commands is enough for most users to model and solve the optimization problems