Ole Morten Aamo

Search for another author

Author Description

Ask a Question About This Mathematician

All published works (47)

Stability and Dissipativity of the Distributed LuGre Friction Model

2025-01-01

Luigi Romano , Ole Morten Aamo , Jan Åslund +1 more

Event-Triggered Boundary Control of Semilinear Hyperbolic Systems

2023-04-07

Timm Strecker , Michael Cantoni , Ole Morten Aamo

In this article, we present an event-triggered boundary control scheme for hyperbolic systems. The trigger condition is based on predictions of the state on determinate sets, and the control input … In this article, we present an event-triggered boundary control scheme for hyperbolic systems. The trigger condition is based on predictions of the state on determinate sets, and the control input is updated only when the predictions deviate from the reference by a given margin. Nominal closed-loop stability, the absence of Zeno behavior, and robustness to uncertainty and disturbances, are all established analytically. For the special case of linear systems, the trigger condition can be expressed in closed-form as an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2}$</tex-math></inline-formula> -scalar product of kernels with the distributed state. The presented controller can also be combined with existing observers to solve the event-triggered output-feedback control problem. A numerical simulation demonstrates the effectiveness of the proposed approach.

Predictive feedback boundary control of semilinear and quasilinear 2 × 2 hyperbolic PDE–ODE systems

2022-04-01

Timm Strecker , Ole Morten Aamo , Michael Cantoni

Chat View PDF

Event-triggered boundary control of 2x2 semilinear hyperbolic systems

2022-01-01

Timm Strecker , Michael Cantoni , Ole Morten Aamo

We present an event-triggered boundary control scheme for hyperbolic systems. The trigger condition is based on predictions of the state on determinate sets, where the control input is only updated … We present an event-triggered boundary control scheme for hyperbolic systems. The trigger condition is based on predictions of the state on determinate sets, where the control input is only updated if the predictions deviate from the reference by a given margin. Closed-loop stability and absence of Zeno behaviour is established analytically. For the special case of linear systems, the trigger condition can be expressed in closed-form as an $L_2$-scalar product of kernels with the distributed state. The presented controller can also be combined with existing observers to solve the event-triggered output-feedback control problem. A numerical simulation demonstrates the effectiveness of the proposed approach.

Chat View PDF

Minimum time observer designs for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si18.svg"><mml:mrow><mml:mi>n</mml:mi><mml:mo linebreak="goodbreak">+</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:math> linear hyperbolic systems with unilateral, bilateral or pointwise in-domain sensing

2021-06-24

Nils Christian A. Wilhelmsen , Henrik Anfinsen , Ole Morten Aamo

Chat View PDF

Boundary Feedback Control of 2×2 Quasilinear Hyperbolic Systems: Predictive Synthesis and Robustness Analysis

2021-05-25

Timm Strecker , Ole Morten Aamo , Michael Cantoni

We present a predictive feedback control method for a class of quasilinear hyperbolic systems with one boundary control input. Assuming exact model knowledge, convergence to the origin, or tracking at … We present a predictive feedback control method for a class of quasilinear hyperbolic systems with one boundary control input. Assuming exact model knowledge, convergence to the origin, or tracking at the uncontrolled boundary, are achieved in finite time. A robustness certificate is provided, showing that at least under more restrictive assumptions on the system coefficients, the control method has inherent robustness properties with respect to small errors in the model, measurements and control input. Rigorous, although conservative conditions on the time derivative of the initial condition and on the design parameter controlling the convergence speed are given to ensure global existence of the solution for initial conditions with arbitrary infinity-norm.

Chat View PDF

Boundary Feedback Control of 2x2 Quasilinear Hyperbolic Systems: Predictive Synthesis and Robustness Analysis

2021-04-09

Timm Strecker , Ole Morten Aamo , Michael Cantoni

Chat View PDF

Predictive feedback boundary control of semilinear and quasilinear 2x2 hyperbolic PDE-ODE systems

2021-01-01

Timm Strecker , Ole Morten Aamo , Michael Cantoni

We present a control design for semilinear and quasilinear 2x2 hyperbolic partial differential equations with the control input at one boundary and a nonlinear ordinary differential equation coupled to the … We present a control design for semilinear and quasilinear 2x2 hyperbolic partial differential equations with the control input at one boundary and a nonlinear ordinary differential equation coupled to the other. The controller can be designed to asymptotically stabilize the system at an equilibrium or relative to a reference signal. Two related but different controllers for semilinear and general quasilinear systems are presented and the additional challenges in quasilinear systems are discussed. Moreover, we present an observer that estimates the distributed PDE state and the unmeasured ODE state from measurements at the actuated boundary only, which can be used to also solve the output feedback control problem.

Chat View PDF

Adaptive Control of a Linear Hyperbolic PDE with Uncertain Transport Speed and a Spatially Varying Coefficient

2020-09-01

Henrik Anfinsen , Haavard Holta , Ole Morten Aamo

Recently, the first result on backstepping-based adaptive control of a 1-D linear hyperbolic partial differential equation (PDE) with an uncertain transport speed was presented. The system also had an uncertain, … Recently, the first result on backstepping-based adaptive control of a 1-D linear hyperbolic partial differential equation (PDE) with an uncertain transport speed was presented. The system also had an uncertain, constant in-domain coefficient, and the derived controller achieved convergence to zero in the L ∞ -sense in finite time. In this paper, we extend that result to systems with a spatially varying in-domain coefficient, achieving asymptotic convergence to zero in the L ∞ -sense. Additionally, for the case of having a constant in-domain coefficient, the new method is shown to have a slightly improved finite-time convergence time. The theory is illustrated in simulations.

Chat View PDF

Adaptive set-point regulation of linear 2 × 2 hyperbolic systems with application to the kick and loss problem in drilling

2020-06-24

Haavard Holta , Henrik Anfinsen , Ole Morten Aamo

Chat View PDF

Adaptive Observer Design for an n + 1 Hyperbolic PDE with Uncertainty and Sensing on Opposite Ends

2020-05-01

Haavard Holta , Ole Morten Aamo

An adaptive observer design for a system of n + 1 coupled 1-D linear hyperbolic partial differential equations with an uncertain boundary condition is presented, extending previous results by removing … An adaptive observer design for a system of n + 1 coupled 1-D linear hyperbolic partial differential equations with an uncertain boundary condition is presented, extending previous results by removing the need for sensing collocated with the uncertainty. This modification is important and motivated by applications in oil & gas drilling where information about the down-hole situation is crucial in order to prevent or deal with unwanted incidents. Uncertainties are usually present down-hole while measurements are available top-side at the rig, only. Boundedness of the state and parameter estimates is proved in the general case, while convergence to true values requires bounded system states and, for parameter convergence, persistent excitation. The central tool for analysis is the infinitedimensional backstepping method applied in two steps, the first of which is time-invariant, while the second is time-varying induced by the time-varying parameter estimates.

Chat View PDF

Output feedback boundary control of heterodirectional semilinear hyperbolic systems

2020-04-17

Timm Strecker , Ole Morten Aamo , Michael Cantoni

Chat View PDF

Stabilization and tracking control of a time-variant linear hyperbolic PIDE using backstepping

2020-03-12

Henrik Anfinsen , Ole Morten Aamo

Direct predictive control of a first-order quasilinear hyperbolic PDE

2019-01-01

Timm Strecker , Ole Morten Aamo , Michael Cantoni

Adaptive Output-Feedback: Uncertain Boundary Condition

2019-01-01

Henrik Anfinsen , Ole Morten Aamo

We will now consider the $$ n + m $$ system ( 18.1 ), but for simplicity restrict ourselves to constant coefficients, that is $$u_t(x, t) + \varLambda ^+ u_x(x, … We will now consider the $$ n + m $$ system ( 18.1 ), but for simplicity restrict ourselves to constant coefficients, that is $$u_t(x, t) + \varLambda ^+ u_x(x, t) = \varSigma ^{++} u(x, t) + \varSigma ^{+-} v(x, t)$$

Model Reference Adaptive Control

2019-01-01

Henrik Anfinsen , Ole Morten Aamo

We consider here anModel reference adaptive control adaptive version of the output tracking results established in Sect. 3.5 , and solve a model reference adaptive control problem where the goal … We consider here anModel reference adaptive control adaptive version of the output tracking results established in Sect. 3.5 , and solve a model reference adaptive control problem where the goal is to make a measured signal track a reference signal from minimal knowledge of the system parameters. Consider system ( 2.1 ), which we restate here $$u_t(x, t) - \lambda (x) u_x(x, t) = f(x) u(x, t) + g(x) u(0, t) \nonumber + \int _{0}^{x} h(x, \xi ) u(\xi , t) d\xi $$

Introduction

2019-01-01

Henrik Anfinsen , Ole Morten Aamo

We now proceed by investigating systems of coupled linear hyperbolic PDEs. The simplest type of such systems are referred to as $$ 2 \times 2 $$ systems, and consists of … We now proceed by investigating systems of coupled linear hyperbolic PDEs. The simplest type of such systems are referred to as $$ 2 \times 2 $$ systems, and consists of two PDEs convecting in opposite directions. $$u_t(x, t) + \lambda (x) u_x(x, t) = c_{11}(x) u(x, t) + c_{12}(x) v(x, t)$$ $$v_t(x, t) - \mu (x) v_x(x, t) = c_{21}(x) u(x, t) + c_{22}(x) v(x, t)$$ $$u(0, t) = q v(0, t)$$ $$v(1, t) = \rho v(1, t) + U(t)$$ $$u(x, 0) = u_0(x)$$ $$v(x, 0) = v_0(x)$$

Background

2019-01-01

Henrik Anfinsen , Ole Morten Aamo

Systems of hyperbolic partial differential equations (PDEs) describe flow and transport phenomena. Typical examples are transmission lines (Curró, Fusco, Manganaro, J Phys A: Math Theor, 44(33):335205, (2011)), road traffic (Amin, … Systems of hyperbolic partial differential equations (PDEs) describe flow and transport phenomena. Typical examples are transmission lines (Curró, Fusco, Manganaro, J Phys A: Math Theor, 44(33):335205, (2011)), road traffic (Amin, Hante, Baye, Hybrid systems computation and control, Springer, pp 602–605, (2008)), heat exchangers (Xu, Sallet, ESAIM: Control Optim Calc Var, 7:421–442, (2010)) Heat exchangers , oil wells (Landet, Pavlov, Aamo, IEEE Trans Control Syst Technol, 21(4):1340–1351, (2013)), multiphase flowMultiphase flow (Di Meglio, Dynamics and control of slugging in oil production. Ph.D. thesis, MINES ParisTech, (2011)); (Diagne, Diagne, Tang, Krstić, Automatica, 76:345–354, (2017)), time-delaysTime-delay (Krstić, Smyshlyaev, Syst Control Lett, 57(9):750–758, (2008b)) and predator–prey systems ( Wollkind, Math Model, 7:413–428, (1986)), to mention a few. These distributed parameter systems give rise to important estimation and control problems, with methods ranging from the use of control Lyapunov functions (Coron, d'Andréa Novel, Bastin, IEEE Trans Autom Control, 52(1):2–11, (2007)), Riemann invariants (Greenberg, Tsien, J Differ Equ, 52(1):66–75, (1984)), frequency domain approaches (Litrico, Fromion, 45th IEEE conference on decision and control, San Diego, CA, USA, (2006)) and active disturbance rejection control (ADRC) (Gou, Jin, IEEE Trans Autom Control, 60(3):824–830, (2015)). The approach taken in this book makes extensive use of Volterra integral transformations, and is known as the infinite-dimensional backstepping approach.

Minimum Time Disturbance Rejection and Tracking Control of $n+m$ Linear Hyperbolic PDEs

2018-06-01

Henrik Anfinsen , Ole Morten Aamo

We extend recent results regarding disturbance rejection control of n+m linear hyperbolic partial differential equations (PDEs) in a number of ways: 1) We allow spatially varying coefficients; 2) The disturbance … We extend recent results regarding disturbance rejection control of n+m linear hyperbolic partial differential equations (PDEs) in a number of ways: 1) We allow spatially varying coefficients; 2) The disturbance is allowed to enter in the interior of the domain, and; 3) Rejection is achieved in minimum time. Additionally, we solve a tracking problem, where the tracking objective is achieved in finite, minimum time. We use a recently derived Fredholm transformation technique in addition to infinite-dimensional backstepping in our design.

Chat View PDF

Control of a Time-Variant 1-D Linear Hyperbolic PDE Using Infinite-Dimensional Backstepping

2018-06-01

Henrik Anfinsen , Ole Morten Aamo

We derive a state-feedback controller for a scalar 1-D linear hyperbolic partial differential equation (PDE) with a spatially-and time-varying interior-domain parameter. The resulting controller ensures convergence to zero in a … We derive a state-feedback controller for a scalar 1-D linear hyperbolic partial differential equation (PDE) with a spatially-and time-varying interior-domain parameter. The resulting controller ensures convergence to zero in a finite time d 1 , corresponding to the propagation time from one boundary to the other. The control law requires predictions of the in-domain parameter a time d 1 into the future. The state-feedback controller is also combined with a boundary observer into an output-feedback control law. Lastly, under the assumption that the interior-domain parameter can be decoupled into a time-varying and a spatially-varying part, a stabilizing adaptive output-feedback control law is derived for an uncertain spatially varying parameter, stabilizing the system in the L 2 -sense from a single boundary measurement only. All derived controllers are implemented and demonstrated in simulations.

Chat View PDF

Stabilization of a linear hyperbolic PDE with actuator and sensor dynamics

2018-05-31

Henrik Anfinsen , Ole Morten Aamo

Chat View PDF

Two-sided boundary control and state estimation of 2 × 2 semilinear hyperbolic systems

2017-12-01

Timm Strecker , Ole Morten Aamo

We solve the problem of controlling a class of one-dimensional semilinear 2 × 2 hyperbolic systems to the origin in minimum time using actuation at both boundaries of the domain. … We solve the problem of controlling a class of one-dimensional semilinear 2 × 2 hyperbolic systems to the origin in minimum time using actuation at both boundaries of the domain. The control method can also be used to solve a class of tracking problems. For the special case of time-invariant linear systems, the state-feedback control law can be written explicitly as the inner product of kernels with the state. We further design an observer to estimate the distributed state from measurements at both boundaries, also in minimum time. The state-feedback controller and observer are combined to solve the output-feedback control problem. A numerical example is given to demonstrate the controller performance.

Chat View PDF

Adaptive stabilization of linear 2 × 2 hyperbolic PDEs with spatially varying coefficients using swapping

2017-12-01

Henrik Anfinsen , Ole Morten Aamo

We extend recent results on adaptive state feedback stabilization of systems described as linear 2 × 2 hyperbolic partial differential equations (PDEs), by offering a solution for the case of … We extend recent results on adaptive state feedback stabilization of systems described as linear 2 × 2 hyperbolic partial differential equations (PDEs), by offering a solution for the case of having spatially varying in-domain coefficients. Proof of L 2 -boundedness, as well as boundedness and asymptotic convergence to zero pointwise in space for all signals in the closed loop are offered, and the theory is demonstrated in a simulation.

Adaptive Stabilization of $ 2 \times 2$ Linear Hyperbolic Systems With an Unknown Boundary Parameter From Collocated Sensing and Control

2017-05-02

Henrik Anfinsen , Ole Morten Aamo

In this paper, we solve an adaptive control problem for a class of 2 × 2 linear hyperbolic partial differential equations, where sensing and actuation are restricted to the boundary … In this paper, we solve an adaptive control problem for a class of 2 × 2 linear hyperbolic partial differential equations, where sensing and actuation are restricted to the boundary anticollocated with an uncertain parameter. This is done by combining a recently derived adaptive observer for the system states and the uncertain parameter, with an adaptive control law. Proof of L2-boundedness for all signals in the closed loop is given, and the system states are proved to converge to zero pointwise in space. The theory is demonstrated in a simulation.

Boundary control of n + 1 coupled linear hyperbolic PDEs with uncertain boundary parameters

2017-05-01

Henrik Anfinsen , Ole Morten Aamo

We combine a swapping-based adaptive observer with a controller to stabilize a system of n + 1 coupled linear hyperbolic partial differential equations (PDEs) with uncertain boundary parameters from boundary … We combine a swapping-based adaptive observer with a controller to stabilize a system of n + 1 coupled linear hyperbolic partial differential equations (PDEs) with uncertain boundary parameters from boundary sensing only. Boundedness of all signals in the closed loop system in the L 2 -sense is proved. The theory is demonstrated in a simulation.

Estimation of boundary parameters in general heterodirectional linear hyperbolic systems

2017-03-02

Henrik Anfinsen , Mamadou Diagne , Ole Morten Aamo +1 more

Adaptive Output Feedback Stabilization of $n + m$ Coupled Linear Hyperbolic PDEs with Uncertain Boundary Conditions

2017-01-01

Henrik Anfinsen , Ole Morten Aamo

We combine a swapping-based adaptive observer with a backstepping-based control law to stabilize a system of $ n + m $ coupled linear hyperbolic partial differential equations (PDEs) with uncertain … We combine a swapping-based adaptive observer with a backstepping-based control law to stabilize a system of $ n + m $ coupled linear hyperbolic partial differential equations (PDEs) with uncertain boundary parameters, using boundary sensing only. Proof of boundedness and square integrability in the $ L_2 $-sense of all signals in the closed loop is given, and the theory is demonstrated in a simulation.

Disturbance rejection in general heterodirectional 1-D linear hyperbolic systems using collocated sensing and control

2016-12-09

Henrik Anfinsen , Ole Morten Aamo

Rejecting Unknown Harmonic Disturbances in $ 2 \times 2 $ Linear Hyperbolic PDEs

2016-12-09

Henrik Anfinsen , Timm Strecker , Ole Morten Aamo

In this paper, we solve the problem of rejecting a harmonic disturbance containing unknown frequencies and bias entering a linear hyperbolic system of 1-D partial differential equations at one boundary, … In this paper, we solve the problem of rejecting a harmonic disturbance containing unknown frequencies and bias entering a linear hyperbolic system of 1-D partial differential equations at one boundary, using boundary sensing and actuation anticollocated with the disturbance. By combining a full state feedback controller with an adaptive observer that estimates system states and the disturbance's bias, frequencies, amplitudes, and phases with exponential convergence, the effect of the disturbance is rejected exponentially fast. The theoretical results are applied to a relevant problem from the oil and gas industry, and the performance is demonstrated in a computer simulation.

Stabilization of a linear 2 × 2 hyperbolic system with an uncertain boundary parameter from collocated sensing and control

2016-10-01

Henrik Anfinsen , Ole Morten Aamo

We establish a control law that manages to adaptively stabilize a system of 2 × 2 linear hyperbolic partial differential equations (PDEs) from sensing and control anti-collocated with an uncertain … We establish a control law that manages to adaptively stabilize a system of 2 × 2 linear hyperbolic partial differential equations (PDEs) from sensing and control anti-collocated with an uncertain boundary parameter. We do this by combining a recently derived adaptive observer with a backstepping-based control law, and prove closed loop stability in the L 2 -sense. The theory is demonstrated in a simulation.

Stabilization of a linear 2 × 2 hyperbolic system with uncertain parameters from anti-collocated sensing and control

2016-10-01

Henrik Anfinsen , Ole Morten Aamo

Using a series of invertible transformations, we bring a system of 2 × 2 linear hyperbolic partial differential equations (PDEs) to an observer canonical form. With transport delays as the … Using a series of invertible transformations, we bring a system of 2 × 2 linear hyperbolic partial differential equations (PDEs) to an observer canonical form. With transport delays as the only information assumed known about the system parameters, a filter based adaptive output feedback control law is designed for the transformed system. Pointwise boundedness of all signals in the closed loop system and pointwise convergence of the system states to zero are established. The theory is demonstrated in a simulation.

A swapping design based adaptive observer for n + 1 coupled linear hyperbolic PDEs

2016-07-01

Henrik Anfinsen , Mamadou Diagne , Ole Morten Aamo +1 more

In this paper, we use swapping design filters to bring systems of n + 1 coupled partial differential equations of the hyperbolic type to static form. Standard parameter identification laws … In this paper, we use swapping design filters to bring systems of n + 1 coupled partial differential equations of the hyperbolic type to static form. Standard parameter identification laws can then be applied to estimate unknown parameters in the boundary conditions. Proof of boundedness of the adaptive laws are offered, and the results are demonstrated in simulations.

Estimating the left boundary condition of coupled 1-D linear hyperbolic PDEs from right boundary sensing

2016-06-01

Henrik Anfinsen , Florent Di Meglio , Ole Morten Aamo

In this paper, we develop an adaptive observer for n + 1 coupled first-order 1-D hyperbolic PDEs for estimation of unknown parameters appearing in the left boundary condition using only … In this paper, we develop an adaptive observer for n + 1 coupled first-order 1-D hyperbolic PDEs for estimation of unknown parameters appearing in the left boundary condition using only measurements at the right boundary. Proof of boundedness of the estimated parameters and sufficient conditions for convergence are offered and the result is demonstrated in a simulation.

Boundary observer design for hyperbolic PDE–ODE cascade systems

2016-02-22

Agus Hasan , Ole Morten Aamo , Miroslav Krstić

An Adaptive Observer Design for $n+1$ Coupled Linear Hyperbolic PDEs Based on Swapping

2016-02-15

Henrik Anfinsen , Mamadou Diagne , Ole Morten Aamo +1 more

In this paper, we use swapping design filters to bring systems of n+1 partial differential equations of the hyperbolic type to static form. Standard parameter identification laws can then be … In this paper, we use swapping design filters to bring systems of n+1 partial differential equations of the hyperbolic type to static form. Standard parameter identification laws can then be applied to estimate unknown parameters in the boundary conditions. Proof of boundedness of the adaptive laws are offered, and the results are demonstrated in simulations.

Boundary Parameter and State Estimation in General Linear Hyperbolic PDEs

2016-01-01

Henrik Anfinsen , Mamadou Diagne , Ole Morten Aamo +1 more

We develop an adaptive observer that estimates boundary parameters and the system states in general heterodirectional linear systems of m+n coupled hyperbolic partial differential equations. The observer uses boundary sensing … We develop an adaptive observer that estimates boundary parameters and the system states in general heterodirectional linear systems of m+n coupled hyperbolic partial differential equations. The observer uses boundary sensing only, and is based on the swapping design, where filters are constructed that can be used to express the system states as linear static combinations of the unknown parameters and the filters states. Standard parameter identification laws can then be applied. Proof of boundedness of the estimates is offered, and sufficient conditions ensuring exponential convergence to their true values is derived. The theory is verified in a simulation.

Tracking in Minimum Time in General Linear Hyperbolic PDEs Using Collocated Sensing and Control

2016-01-01

Henrik Anfinsen , Ole Morten Aamo

We solve a tracking problem for general heterodirectional linear 1-D hyperbolic partial differential equations. A full state feedback controller and an observer generating full state estimates from sensing co-located with … We solve a tracking problem for general heterodirectional linear 1-D hyperbolic partial differential equations. A full state feedback controller and an observer generating full state estimates from sensing co-located with the actuation are designed. Both converge in finite, minimum time. The two are then combined into an output feedback law achieving tracking in finite time given by the sum of the convergence times of the controller and observer.

Disturbance Rejection in n + 1 Coupled 1-D Linear Hyperbolic PDEs Using Collocated Sensing and Control

2016-01-01

Henrik Anfinsen , Ole Morten Aamo

We derive a full state feedback law and a state observer for a class of disturbance rejection problems for n+1 linear coupled partial differential equations (PDEs). The disturbance enters the … We derive a full state feedback law and a state observer for a class of disturbance rejection problems for n+1 linear coupled partial differential equations (PDEs). The disturbance enters the system at one boundary, while the actuation and sensing are limited to the opposite boundary. We solve this by separately designing a state feedback controller and an observer, and show that they can be combined into an output feedback control law that rejects the effect of the disturbance with exponential decay. The performance of output feedback controller is demonstrated in a simulation.

Disturbance Rejection in the Interior Domain of Linear 2 <inline-formula> <tex-math notation="TeX">$\times$</tex-math></inline-formula> 2 Hyperbolic Systems

2014-05-07

Henrik Anfinsen , Ole Morten Aamo

In this technical note, we develop a full state feedback law for disturbance rejection in systems described by linear 2 × 2 partial differential equations of the hyperbolic type, with … In this technical note, we develop a full state feedback law for disturbance rejection in systems described by linear 2 × 2 partial differential equations of the hyperbolic type, with the disturbance modelled as an autonomous, finite dimensional linear system affecting the PDE's left boundary, and actuation limited to the right boundary. The effect of the disturbance is rejected at an arbitrary point in the domain within a finite time. The performance is demonstrated through simulation.

Rejection of Heave-Induced Pressure Fluctuations at the Casing Shoe in Managed Pressure Drilling

2014-01-01

Henrik Anfinsen , Ole Morten Aamo

Global boundary feedback stabilization for a class of pseudo-parabolic partial differential equations

2013-06-01

Agus Hasan , Ole Morten Aamo , Bjarne Foss

This paper considers the boundary stabilization problem for a class of nonlinear pseudo-parabolic partial differential equations. The proposed control laws are used to achieve semi-global exponential stability for the nonlinear … This paper considers the boundary stabilization problem for a class of nonlinear pseudo-parabolic partial differential equations. The proposed control laws are used to achieve semi-global exponential stability for the nonlinear systems in the H 1 -sense. An H 2 bound of the solution for the nonlinear systems is also derived. A numerical example is included to illustrate the application of the proposed control laws.

Disturbance rejection in 2 x 2 linear hyperbolic systems

2012-11-16

Ole Morten Aamo

Many interesting problems in the oil and gas industry face the challenge of responding to disturbances from afar. Typically, the disturbance occurs at the inlet of a pipeline or the … Many interesting problems in the oil and gas industry face the challenge of responding to disturbances from afar. Typically, the disturbance occurs at the inlet of a pipeline or the bottom of an oil well, while sensing and actuation equipment is installed at the outlet, only, kilometers away from the disturbance. The present paper develops an output feedback control law for such cases, based on modelling the transport phenomenon as a 2 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\times$</tex></formula> 2 linear partial differential equation (PDE) of hyperbolic type and the disturbance as a finite-dimensional linear system affecting the left boundary of the PDE. Sensing and actuation are co-located at the right boundary of the PDE. The design provides a separation principle, allowing a disturbance attenuating full-state feedback control law to be combined with an observer. The results are applied to a relevant problem from the oil and gas industry and demonstrated in simulations.

Rejecting disturbances by output feedback in linear hyperbolic systems

2012-11-01

Ole Morten Aamo

Many interesting problems in the oil and gas industry face the challenge of responding to disturbances from afar. Typically, the disturbance occurs at the inlet of a pipeline or the … Many interesting problems in the oil and gas industry face the challenge of responding to disturbances from afar. Typically, the disturbance occurs at the inlet of a pipeline or the bottom of an oil well, while sensing and actuation equipment is installed at the outlet, only, kilometers away from the disturbance. The present paper develops an output feedback control law for such cases, based on modelling the transport phenomenon as a 2×2 linear partial differential equation (PDE) of hyperbolic type and the disturbance as a finite-dimensional linear system affecting the left boundary of the PDE. Sensing and actuation are co-located at the right boundary of the PDE. The design provides a separation principle, allowing a disturbance attenuating full-state feedback control law to be combined with an observer.

Boundary control of long waves in nonlinear dispersive systems

2011-12-29

Agus Hasan , Bjarne Foss , Ole Morten Aamo

Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well … Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases.

A constructive speed observer design for general Euler–Lagrange systems

2011-08-26

Øyvind Nistad Stamnes , Ole Morten Aamo , Glenn‐Ole Kaasa

Boundary Control of the Linearized Ginzburg--Landau Model of Vortex Shedding

2005-01-01

Ole Morten Aamo , Andrey Smyshlyaev , Miroslav Krstić

In this paper, we continue the development of state feedback boundary control laws based on the backstepping methodology, for the stabilization of unstable, parabolic partial differential equations. We consider the … In this paper, we continue the development of state feedback boundary control laws based on the backstepping methodology, for the stabilization of unstable, parabolic partial differential equations. We consider the linearized Ginzburg--Landau equation, which models, for instance, vortex shedding in bluff body flows. Asymptotic stabilization is achieved by means of boundary control via state feedback in the form of an integral operator. The kernel of the operator is shown to be twice continuously differentiable, and a series approximation for its solution is given. Under certain conditions on the parameters of the Ginzburg--Landau equation, compatible with vortex shedding modelling on a semi-infinite domain, the kernel is shown to have compact support, resulting in partial state feedback. Simulations are provided in order to demonstrate the performance of the controller. In summary, the paper extends previous work in two ways: (1) it deals with two coupled partial differential equations, and (2) under certain circumstances handles equations defined on a semi-infinite domain.

Governing Equations

2003-01-01

Ole Morten Aamo , Miroslav Krstić

We will be studying the behavior of a fluid contained in the domain Ω, as shown schematically in Figure 2.1. Associated with the fluid is its density, ρ : Ω … We will be studying the behavior of a fluid contained in the domain Ω, as shown schematically in Figure 2.1. Associated with the fluid is its density, ρ : Ω × ℝ+→ ℝ. At every time instant t > 0, and to every point p ∈ Ω, we assign a vector valued quantity which is the velocity, W, of the fluid at that point in time and space. That is, we are interested in the evolution of a vector field W : Ω× ℝ+→ ℝn, where n is thedimension of the problem. Associated with the velocity field is a pressure field, which is a scalar valued function P : Ω × ℝ+→ ℝ. We will study problems in 2 and 3 dimensions (2D and 3D), using cartesian and cylindrical coordinates. In cartesian coordinates, we denote a point p ∈ Ω with (x, y) in 2D and (x, y, z) in 3D. In cylindrical coordinates, we denote a point p ∈ Ω with (r, θ, z). The two coordinate systems are shown schematically in Figure 2.1. The velocity field is denoted W(x, y, z, t) = (U(x, y, z, t), V(x, y, z, t), W(x, y, z, t)) in 3D cartesian coordinates, where U ,V,and W are the velocity components in the x, y and z directions, respectively (W (x, y, t) = (U(x, y, t), V(x, y, t)) in 2D). In cylindrical coordinates, we denote the velocity field W (r, θ, z, t) = (V r(x, y, z, t), V θ(x, y, z, t), V z (x, y, z, t)), where Vr, Vθ, and Vz are the velocity components in the r, B and z directions, respectively. The density, ρ, and the pressure, P, take the same arguments as the velocity, but are scalar valued. Below we will derive the conservation equations in cartesian coordinates, and state the corresponding equations in cylindrical coordinates. The derivation follows [31].

Common Coauthors

Coauthor	Papers Together
Henrik Anfinsen	28
Timm Strecker	10
Michael Cantoni	8
Miroslav Krstić	7
Mamadou Diagne	4
Agus Hasan	3
Haavard Holta	3
Bjarne Foss	2
Florent Di Meglio	1
Luigi Romano	1
Erik Frisk	1
Andrey Smyshlyaev	1
Jan Åslund	1
Nils Christian A. Wilhelmsen	1
Øyvind Nistad Stamnes	1
Glenn‐Ole Kaasa	1

Commonly Cited References

Backstepping boundary control for first-order hyperbolic PDEs and application to systems with actuator and sensor delays

2008-04-09

Miroslav Krstić , Andrey Smyshlyaev

Control of Homodirectional and General Heterodirectional Linear Coupled Hyperbolic PDEs

2015-12-28

Long Hu , Florent Di Meglio , Rafael Vázquez +1 more

Research on stabilization of coupled hyperbolic PDEs has been dominated by the focus on pairs of counter-convecting (“heterodirectional”) transport PDEs with distributed local coupling and with controls at one or … Research on stabilization of coupled hyperbolic PDEs has been dominated by the focus on pairs of counter-convecting (“heterodirectional”) transport PDEs with distributed local coupling and with controls at one or both boundaries. A recent extension allows stabilization using only one control for a system containing an arbitrary number of coupled transport PDEs that convect at different speeds against the direction of the PDE whose boundary is actuated. In this paper we present a solution to the fully general case, in which the number of PDEs in either direction is arbitrary, and where actuation is applied on only one boundary (to all the PDEs that convect downstream from that boundary). To solve this general problem, we solve, as a special case, the problem of control of coupled “homodirectional” hyperbolic linear PDEs, where multiple transport PDEs convect in the same direction with arbitrary local coupling. Our approach is based on PDE backstepping and yields solutions to stabilization, by both full-state and observer-based output feedback, and trajectory tracking problems.

Chat View PDF

Disturbance rejection in 2 x 2 linear hyperbolic systems

2012-11-16

Ole Morten Aamo

Stabilization of a System of <formula formulatype="inline"> <tex Notation="TeX">$n+1$</tex></formula> Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input

2013-08-01

Florent Di Meglio , Rafael Vázquez , Miroslav Krstić

We solve the problem of stabilization of a class of linear first-order hyperbolic systems featuring n rightward convecting transport PDEs and one leftward convecting transport PDE. We design a controller, … We solve the problem of stabilization of a class of linear first-order hyperbolic systems featuring n rightward convecting transport PDEs and one leftward convecting transport PDE. We design a controller, which requires a single control input applied on the leftward convecting PDE's right boundary, and an observer, which employs a single sensor on the same PDE's left boundary. We prove exponential stability of the origin of the resulting plant-observer-controller system in the spatial L 2 -sense.

Boundary Feedback Stabilization of an Unstable Heat Equation

2003-01-01

Weijiu Liu

In this paper we study the problem of boundary feedback stabilization for the unstable heat equation ut(x,t) = uxx(x,t)+a(x) u(x,t). This equation can be viewed as a model of a … In this paper we study the problem of boundary feedback stabilization for the unstable heat equation ut(x,t) = uxx(x,t)+a(x) u(x,t). This equation can be viewed as a model of a heat conducting rod in which not only is the heat being diffused (mathematically due to the diffusive term uxx) but also the destabilizing heat is generating (mathematically due to the term a u with a >0). We show that for any given continuously differentiable function a and any given positive constant $\l$ we can explicitly construct a boundary feedback control law such that the solution of the equation with the control law converges to zero exponentially at the rate of $\l$. This is a continuation of the recent work of Boskovic, Krstic, and Liu [IEEE Trans. Automat. Control, 46 (2001), pp. 2022--2028] and Balogh and Krstic [European J. Control, 8 (2002), pp. 165--176].

The effect of boundary damping for the quasilinear wave equation

1984-03-01

J. M. Greenberg , Li Ta Tsien

Boundary control of an unstable heat equation via measurement of domain-averaged temperature

2001-01-01

Dejan M. Bošković , Miroslav Krstić , Weijiu Liu

In this note, a feedback boundary controller for an unstable heat equation is designed. The equation can be viewed as a model of a thin rod with not only the … In this note, a feedback boundary controller for an unstable heat equation is designed. The equation can be viewed as a model of a thin rod with not only the heat loss to a surrounding medium (stabilizing) but also the heat generation inside the rod (destabilizing). The heat generation adds a destabilizing linear term on the right-hand side of the equation. The boundary control law designed is in the form of an integral operator with a known, continuous kernel function but can be interpreted as a backstepping control law. This interpretation provides a Lyapunov function for proving stability of the system. The control is applied by insulating one end of the rod and applying either Dirichlet or Neumann boundary actuation on the other.

Adaptive output-feedback stabilization of non-local hyperbolic PDEs

2014-09-26

Pauline Bernard , Miroslav Krstić

Disturbance Rejection in the Interior Domain of Linear 2 <inline-formula> <tex-math notation="TeX">$\times$</tex-math></inline-formula> 2 Hyperbolic Systems

2014-05-07

Henrik Anfinsen , Ole Morten Aamo

On Stability of Switched Linear Hyperbolic Conservation Laws with Reflecting Boundaries

2008-07-17

Saurabh Amin , Falk M. Hante , Alexandre M. Bayen

A reduction procedure for generalized Riemann problems with application to nonlinear transmission lines

2011-07-25

Carmela Currò , D. Fusco , N. Manganaro

Generalized simple wave solutions to quasilinear hyperbolic nonhomogeneous systems of PDEs are obtained through the differential constraint method. These solutions prove to be flexible enough to solve generalized Riemann problems … Generalized simple wave solutions to quasilinear hyperbolic nonhomogeneous systems of PDEs are obtained through the differential constraint method. These solutions prove to be flexible enough to solve generalized Riemann problems where discontinuous initial data are involved. Within such a theoretical framework, the governing model of nonlinear transmission lines is investigated throughout.

Boundary Estimation of Boundary Parameters for Linear Hyperbolic PDEs

2016-12-21

Michelangelo Bin , Florent Di Meglio

We propose an adaptive observer scheme to estimate boundary parameters in first-order hyperbolic systems of Partial Differential Equations (PDE). The considered systems feature an arbitrary number of states traveling in … We propose an adaptive observer scheme to estimate boundary parameters in first-order hyperbolic systems of Partial Differential Equations (PDE). The considered systems feature an arbitrary number of states traveling in one direction and one counter-convecting state. Uncertainties in the boundary reflection coefficients and boundary additive errors are estimated relying on a pre-existing observer design and a novel Lyapunov-based adaptation law.

Adaptive boundary stabilization for first‐order hyperbolic PDEs with unknown spatially varying parameter

2015-03-13

Zaihua Xu , Yungang Liu

Summary The adaptive boundary stabilization is investigated for a class of systems described by first‐order hyperbolic PDEs with unknown spatially varying parameter. Towards the system unknowns, a dynamic compensation is … Summary The adaptive boundary stabilization is investigated for a class of systems described by first‐order hyperbolic PDEs with unknown spatially varying parameter. Towards the system unknowns, a dynamic compensation is first given by using infinite‐dimensional backstepping method, adaptive techniques, and projection operator. Then an adaptive controller is constructed by certainty equivalence principle, which can stabilize the original system in a certain sense. Moreover, the effectiveness of the proposed method is illustrated by a simulation example. Copyright © 2015 John Wiley & Sons, Ltd.

Local Exponential $H^2$ Stabilization of a $2\times2$ Quasilinear Hyperbolic System Using Backstepping

2013-01-01

Jean‐Michel Coron , Rafael Vázquez , Miroslav Krstić +1 more

In this work, we consider the problem of boundary stabilization for a quasilinear $2\times2$ system of first-order hyperbolic PDEs. We design a new full-state feedback control law, with actuation on … In this work, we consider the problem of boundary stabilization for a quasilinear $2\times2$ system of first-order hyperbolic PDEs. We design a new full-state feedback control law, with actuation on only one end of the domain, which achieves $H^2$ exponential stability of the closed-loop system. Our proof uses a backstepping transformation to find new variables for which a strict Lyapunov function can be constructed. The kernels of the transformation are found to verify a Goursat-type $4\times4$ system of first-order hyperbolic PDEs, whose well-posedness is shown using the method of characteristics and successive approximations. Once the kernels are computed, the stabilizing feedback law can be explicitly constructed from them.

Chat View PDF

Boundary Stabilization of a 1-D Wave Equation with In-Domain Antidamping

2010-01-01

Andrey Smyshlyaev , Eduardo Cerpa , Miroslav Krstić

We consider the problem of boundary stabilization of a 1-D (one-dimensional) wave equation with an internal spatially varying antidamping term. This term puts all the eigenvalues of the open-loop system … We consider the problem of boundary stabilization of a 1-D (one-dimensional) wave equation with an internal spatially varying antidamping term. This term puts all the eigenvalues of the open-loop system in the right half of the complex plane. We design a feedback law based on the backstepping method and prove exponential stability of the closed-loop system with a desired decay rate. For plants with constant parameters the control gains are found in closed form. Our design also produces a new Lyapunov function for the classical wave equation with passive boundary damping.

An Adaptive Observer Design for $n+1$ Coupled Linear Hyperbolic PDEs Based on Swapping

2016-02-15

Henrik Anfinsen , Mamadou Diagne , Ole Morten Aamo +1 more

Backstepping stabilization of the linearized Saint-Venant–Exner model

2016-12-08

Ababacar Diagne , Mamadou Diagne , Shu‐Xia Tang +1 more

Chat View PDF

An adaptive observer for hyperbolic systems with application to UnderBalanced Drilling

2014-01-01

Florent Di Meglio , Delphine Bresch‐Pietri , Ulf Jakob F. Aarsnes

Chat View PDF

Minimum time control of heterodirectional linear coupled hyperbolic PDEs

2016-06-10

Jean Auriol , Florent Di Meglio

Chat View PDF

Adaptive boundary control for unstable parabolic PDEs—Part II: Estimation-based designs

2007-07-24

Andrey Smyshlyaev , Miroslav Krstić

Exact Boundary Controllability for Quasi-Linear Hyperbolic Systems

2003-01-01

Tatsien Li , Bopeng Rao

Using a result on the existence and uniqueness of the semiglobal C1 solution to the mixed initial-boundary value problem for first order quasi-linear hyperbolic systems with general nonlinear boundary conditions, … Using a result on the existence and uniqueness of the semiglobal C1 solution to the mixed initial-boundary value problem for first order quasi-linear hyperbolic systems with general nonlinear boundary conditions, we establish the exact boundary controllability for quasi-linear hyperbolic systems if the C1 norm of initial and final states is small enough.

Disturbance Rejection in n + 1 Coupled 1-D Linear Hyperbolic PDEs Using Collocated Sensing and Control

2016-01-01

Henrik Anfinsen , Ole Morten Aamo

Disturbance rejection in general heterodirectional 1-D linear hyperbolic systems using collocated sensing and control

2016-12-09

Henrik Anfinsen , Ole Morten Aamo

Disturbance attenuation of n + 1 coupled hyperbolic PDEs

2014-12-01

Agus Hasan

In this paper, we present a state-feedback and a state-observer for disturbance attenuation problems for a class of n + 1 coupled linear hyperbolic partial differential equations. The disturbance and … In this paper, we present a state-feedback and a state-observer for disturbance attenuation problems for a class of n + 1 coupled linear hyperbolic partial differential equations. The disturbance and the sensing are located at the left boundary of the system while the actuation is located at the right boundary of the system (anti-collocated setup). The designs are based on the backstepping method and rely on boundary measurement only. The feedback control law is found by utilizing the fact that the closed-form solution of the equivalent target system can be obtained. Furthermore, by defining a modified L 2 -norm, we show the observer is exponentially stable. A numerical example inspired from an oil well drilling problem is presented to validate the results.

Chat View PDF

Stability and Boundary Stabilization of 1-D Hyperbolic Systems

2016-01-01

Georges Bastin , Jean‐Michel Coron

This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for

Control of 1-D parabolic PDEs with Volterra nonlinearities, Part I: Design

2008-09-27

Rafael Vázquez , Miroslav Krstić

Chat View PDF

Closed-Form Boundary State Feedbacks for a Class of 1-D Partial Integro-Differential Equations

2004-12-01

Andrey Smyshlyaev , Miroslav Krstić

In this paper, a problem of boundary stabilization of a class of linear parabolic partial integro-differential equations (P(I)DEs) in one dimension is considered using the method of backstepping, avoiding spatial … In this paper, a problem of boundary stabilization of a class of linear parabolic partial integro-differential equations (P(I)DEs) in one dimension is considered using the method of backstepping, avoiding spatial discretization required in previous efforts. The problem is formulated as a design of an integral operator whose kernel is required to satisfy a hyperbolic P(I)DE. The kernel P(I)DE is then converted into an equivalent integral equation and by applying the method of successive approximations, the equation's well posedness and the kernel's smoothness are established. It is shown how to extend this approach to design optimally stabilizing controllers. An adaptation mechanism is developed to reduce the conservativeness of the inverse optimal controller, and the performance bounds are derived. For a broad range of physically motivated special cases feedback laws are constructed explicitly and the closed-loop solutions are found in closed form. A numerical scheme for the kernel P(I)DE is proposed; its numerical effort compares favorably with that associated with operator Riccati equations.

Chat View PDF

Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions

1978-10-01

David L. Russell

This paper is an assessment of the current state of controllability and observability theories for linear partial differential equations, summarizing existing results and indicating open problems in the area. The … This paper is an assessment of the current state of controllability and observability theories for linear partial differential equations, summarizing existing results and indicating open problems in the area. The emphasis is placed on hyperbolic and parabolic systems. Related subjects such as spectral determination, control of nonlinear equations, linear quadratic cost criteria and time optimal control are also discussed.

Finite-time output regulation for linear 2×2 hyperbolic systems using backstepping

2016-11-02

Joachim Deutscher

Global boundary controllability of the de St. Venant equations between steady states

2003-02-01

Martin Gugat , Günter Leugering

Chat View PDF

Output feedback boundary control of heterodirectional semilinear hyperbolic systems

2020-04-17

Timm Strecker , Ole Morten Aamo , Michael Cantoni

Chat View PDF

Boundary Controllability of Nonlinear Hyperbolic Systems

1969-05-01

M. Cirinà

Previous article Next article Boundary Controllability of Nonlinear Hyperbolic SystemsMarco CirinàMarco Cirinàhttps://doi.org/10.1137/0307014PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. G. Butkovskii and , L. N. Poltavskii, Optimal control of wave … Previous article Next article Boundary Controllability of Nonlinear Hyperbolic SystemsMarco CirinàMarco Cirinàhttps://doi.org/10.1137/0307014PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. G. Butkovskii and , L. N. Poltavskii, Optimal control of wave processes, Avtomat. i Telemekh., 27 (1966), 48–53 Google Scholar[2] M. Cirina, Nonlinear hyperbolic problems: a priori bounds and solutions on preassigned sets, Rep., 960, University of Wisconsin, Math. Res. Center, Madison, Wisconsin Google Scholar[3] Roberto Conti, On some aspects of linear control theoryMathematical Theory of Control (Proc. Conf., Los Angeles, Calif., 1967), Academic Press, New York, 1967, 285–300 MR0275942 0224.93022 Google Scholar[4] H. O. Fattorini, Time optimal control of solutions of operational differenital equations, SIAM J. Control, 2 (1964), 54–59 10.1137/0302005 LinkGoogle Scholar[5] H. O. Fattorini, Boundary control systems, SIAM J. Control, 6 (1968), 349–385 10.1137/0306025 MR0239249 0164.10902 LinkISIGoogle Scholar[6] G. D. Johnson, Masters Thesis, On a nonlinear vibrating string, Doctoral thesis, University of California, Los Angeles, 1967 Google Scholar[7] Herbert B. Keller and , Vidar Thomée, Unconditionally stable difference methods for mixed problems for quasi-linear hyperbolic systems in two dimensions, Comm. Pure Appl. Math., 15 (1962), 63–73 MR0158555 0109.09603 CrossrefISIGoogle Scholar[8] Heinz-Otto Kreiss, D. Greenspan, Difference approximations for the initial-boundary value problem for hyperbolic differential equationsNumerical Solutions of Nonlinear Differential Equations (Proc. Adv. Sympos., Madison, Wis., 1966), John Wiley & Sons Inc., New York, 1966, 141–166 MR0214305 0161.12502 Google Scholar[9A] Jacques-Louis Lions, Sur le contrôle optimal de systèmes décrits par des équations aux dérivées partielles linéaires. Remarques générales, C. R. Acad. Sci. Paris Sér. A-B, 263 (1966), A661–A663 MR0214896 0148.07705 ISIGoogle Scholar[9B] Jacques-Louis Lions, Sur le contrôle optimal de systèmes décrits par des équations aux dérivées partielles linéaires. Équations elliptiques, C. R. Acad. Sci. Paris Sér. A-B, 263 (1966), A713–A715 MR0214897 0148.07801 ISIGoogle Scholar[9C] Jacques-Louis Lions, Sur le contrôle optimal de systèmes décrits par des équations aux dérivées partielles linéaires. Équations d'évolution, C. R. Acad. Sci. Paris Sér. A-B, 263 (1966), A776–A779 MR0214898 0148.07802 ISIGoogle Scholar[10] L. Markus, Controllability of nonlinear processes, SIAM J. Control, 3 (1965), 78–90 10.1137/0303008 LinkGoogle Scholar[11] David L. Russell, Optimal regulation of linear symmetric hyperbolic systems with finite dimensional controls, SIAM J. Control, 4 (1966), 276–294 10.1137/0304024 MR0195619 0166.35805 LinkGoogle Scholar[12] David L. Russell, On boundary-value controllability of linear symmetric hyperbolic systemsMathematical Theory of Control (Proc. Conf., Los Angeles, Calif., 1967), Academic Press, New York, 1967, 312–321 MR0258500 0214.39607 Google Scholar[13] Vidar Thomée, A stable difference scheme for the mixed boundary problem for a hyperbolic, first-order system in two dimensions, J. Soc. Indust. Appl. Math., 10 (1962), 229–245 MR0154422 0107.11401 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Internal Controllability of First Order Quasi-linear Hyperbolic Systems with a Reduced Number of ControlsSIAM Journal on Control and Optimization, Vol. 55, No. 1 | 8 February 2017AbstractPDF (510 KB)Infinite-Dimensional Predictive Control for Hyperbolic SystemsSIAM Journal on Control and Optimization, Vol. 52, No. 6 | 13 November 2014AbstractPDF (578 KB)Some Results on the Controllability of Coupled Semilinear Wave Equations: The Desensitizing Control CaseSIAM Journal on Control and Optimization, Vol. 49, No. 3 | 24 May 2011AbstractPDF (250 KB)Global Controllability of Nonviscous and Viscous Burgers-Type EquationsSIAM Journal on Control and Optimization, Vol. 48, No. 3 | 1 May 2009AbstractPDF (312 KB)Optimal Control in Networks of Pipes and CanalsSIAM Journal on Control and Optimization, Vol. 48, No. 3 | 10 June 2009AbstractPDF (300 KB)Exact Controllability for Multidimensional Semilinear Hyperbolic EquationsSIAM Journal on Control and Optimization, Vol. 46, No. 5 | 17 October 2007AbstractPDF (349 KB)Boundary Controllability between Sub- and Supercritical FlowSIAM Journal on Control and Optimization, Vol. 42, No. 3 | 26 July 2006AbstractPDF (275 KB)Exact Boundary Controllability for Quasi-Linear Hyperbolic SystemsSIAM Journal on Control and Optimization, Vol. 41, No. 6 | 26 July 2006AbstractPDF (117 KB)Exact Controllability Theorems and Numerical Simulations for Some Nonlinear Differential EquationsSIAM Journal on Control and Optimization, Vol. 19, No. 6 | 17 February 2012AbstractPDF (1902 KB)Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open QuestionsSIAM Review, Vol. 20, No. 4 | 17 February 2012AbstractPDF (9779 KB)A General Theory of Observation and ControlSIAM Journal on Control and Optimization, Vol. 15, No. 2 | 18 July 2006AbstractPDF (2824 KB)Controllability of the Nonlinear Wave Equation in Several Space VariablesSIAM Journal on Control and Optimization, Vol. 14, No. 1 | 3 August 2006AbstractPDF (634 KB)Boundary Value Control of the Higher-Dimensional Wave EquationSIAM Journal on Control, Vol. 9, No. 1 | 18 July 2006AbstractPDF (1178 KB) Volume 7, Issue 2| 1969SIAM Journal on Control179-365 History Submitted:14 November 1968Published online:18 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0307014Article page range:pp. 198-212ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics

Chat View PDF

Adaptive Stabilization of $ 2 \times 2$ Linear Hyperbolic Systems With an Unknown Boundary Parameter From Collocated Sensing and Control

2017-05-02

Henrik Anfinsen , Ole Morten Aamo

Two-sided boundary control and state estimation of 2 × 2 semilinear hyperbolic systems

2017-12-01

Timm Strecker , Ole Morten Aamo

Chat View PDF

Estimation of boundary parameters in general heterodirectional linear hyperbolic systems

2017-03-02

Henrik Anfinsen , Mamadou Diagne , Ole Morten Aamo +1 more

Infinite Dimensional Backstepping-Style Feedback Transformations for a Heat Equation with an Arbitrary Level of Instability

2002-01-01

András Balogh , Miroslav Krstić

Backstepping observers for a class of parabolic PDEs

2004-12-30

Andrey Smyshlyaev , Miroslav Krstić

Estimating the left boundary condition of coupled 1-D linear hyperbolic PDEs from right boundary sensing

2016-06-01

Henrik Anfinsen , Florent Di Meglio , Ole Morten Aamo

Applications of linear hyperbolic partial differential equations: predator-prey systems and gravitational instability of nebulae

1986-01-01

David J. Wollkind

Semi-globalC1solution and exact boundary controllability for reducible quasilinear hyperbolic systems

2000-03-01

Tatsien Li , Bopeng Rao , Yi Jin

By means of a result on the semi-global C1 solution, we establish the exact boundary controllability for the reducible quasilinear hyperbolic system if the C1 norm of initial data and … By means of a result on the semi-global C1 solution, we establish the exact boundary controllability for the reducible quasilinear hyperbolic system if the C1 norm of initial data and final state is small enough.

Chat View PDF

Delay-Robust Control Design for Two Heterodirectional Linear Coupled Hyperbolic PDEs

2018-01-26

Jean Auriol , Ulf Jakob F. Aarsnes , Philippe Martin +1 more

We detail in this paper the importance of a change of strategy for the delay robust control of systems composed of two linear first-order hyperbolic equations. One must go back … We detail in this paper the importance of a change of strategy for the delay robust control of systems composed of two linear first-order hyperbolic equations. One must go back to the classical tradeoff between convergence rate and delay robustness. More precisely, we prove that, for systems with strong reflections, canceling the reflection at the actuated boundary will yield zero delay robustness. Indeed, for such systems, using a backstepping controller, the corresponding target system should preserve a small amount of this reflection to ensure robustness to a small delay in the loop. This implies, in some cases, giving up finite time convergence.

Chat View PDF

New development in freefem++

2012-01-01

Frédéric Hecht

-This is a short presentation of the freefem++ software. In Section 1, we recall most of the characteristics of the software, In Section 2, we recall how to to build … -This is a short presentation of the freefem++ software. In Section 1, we recall most of the characteristics of the software, In Section 2, we recall how to to build the weak form of a partial differential equation (PDE) from the strong form. In the 3 last sections, we present different examples and tools to illustrated the power of the software. First we deal with mesh adaptation for problems in two and three dimension, second, we solve numerically a problem with phase change and natural convection, and the finally to show the possibilities for HPC we solve a Laplace equation by a Schwarz domain decomposition problem on parallel computer.

Stabilization of a linear 2 × 2 hyperbolic system with uncertain parameters from anti-collocated sensing and control

2016-10-01

Henrik Anfinsen , Ole Morten Aamo

Control of 1D parabolic PDEs with Volterra nonlinearities, Part II: Analysis

2008-10-03

Rafael Vázquez , Miroslav Krstić

Exact boundary observability for quasilinear hyperbolic systems

2008-01-29

Tatsien Li

By means of a direct and constructive method based on the theory of semi-global C1 solution, the local exact boundary observability is established for one-dimensional first order quasilinear hyperbolic systems … By means of a direct and constructive method based on the theory of semi-global C1 solution, the local exact boundary observability is established for one-dimensional first order quasilinear hyperbolic systems with general nonlinear boundary conditions. An implicit duality between the exact boundary controllability and the exact boundary observability is then shown in the quasilinear case.

Chat View PDF

Finite-time boundary stabilization of general linear hyperbolic balance laws via Fredholm backstepping transformation

2017-08-10

Jean‐Michel Coron , Long Hu , Guillaume Olive

Chat View PDF

Time-delayed boundary feedback stabilization of the isothermal Euler equations with friction

2011-01-01

Martin Gugat , Markus Dick

We consider the isothermal Euler equations with friction that modelthe gas flow through pipes. We present a method of time-delayedboundary feedback stabilization to stabilize the isothermal Eulerequations locally around a … We consider the isothermal Euler equations with friction that modelthe gas flow through pipes. We present a method of time-delayedboundary feedback stabilization to stabilize the isothermal Eulerequations locally around a given stationary subcritical state on afinite time interval. The considered control system is a quasilinearhyperbolic system with a source term. For this system we introduce aLyapunov function with delay terms and develop time-delayed boundarycontrols for which the Lyapunov function decays exponentially withtime. We present the stabilization method for a single gas pipe andfor a star-shaped network of pipes.

Chat View PDF

An initial- and boundary-value problem for a model equation for propagation of long waves

1980-06-01

Jerry L. Bona , Vassilios A. Dougalis

Bilateral Boundary Control of One-Dimensional First- and Second-Order PDEs using Infinite-Dimensional Backstepping

2016-03-15

Rafael Vázquez , Miroslav Krstić

This paper develops an extension of infinite-dimensional backstepping method for parabolic and hyperbolic systems in one spatial dimension with two actuators. Typically, PDE backstepping is applied in 1-D domains with … This paper develops an extension of infinite-dimensional backstepping method for parabolic and hyperbolic systems in one spatial dimension with two actuators. Typically, PDE backstepping is applied in 1-D domains with an actuator at one end. Here, we consider the use of two actuators, one at each end of the domain, which we refer to as bilateral control (as opposed to unilateral control). Bilateral control laws are derived for linear reaction-diffusion, wave and 2X2 hyperbolic 1-D systems (with same speed of transport in both directions). The extension is nontrivial but straightforward if the backstepping transformation is adequately posed. The resulting bilateral controllers are compared with their unilateral counterparts in the reaction-diffusion case for constant coefficients, by making use of explicit solutions, showing a reduction in control effort as a tradeoff for the presence of two actuators when the system coefficients are large. These results open the door for more sophisticated designs such as bilateral sensor/actuator output feedback and fault-tolerant designs.

Chat View PDF

Nonlinear hyperbolic problems with solutions on preassigned sets.

1970-09-01

M. Cirinà