An Optimal Control Approach for Hybrid Systems

Riedinger, Pierre; Lung, Chung-Horng; Kratz, Frédéric

doi:10.3166/ejc.9.449-458

Cited by 75 publications

(36 citation statements)

References 14 publications

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“…Classically, we formulate the optimal control switching problem as an optimal control problem with artificial controls being functions of time, each valued in the discrete set {0, 1}, and we relax it into a control problem with such controls now valued in the interval [0,1]. In contrast with existing approaches following this relaxation strategy, see, e.g., [4,37], relying on the local Pontryagin maximum principle, our aim is to apply the global approach of [28]. We show that by specializing the convex objects for switched systems, one obtains a numerical method for which the number of modes driving the system enters linearly into the complexity of the problem, instead of exponentially.…”

Section: Introductionmentioning

confidence: 99%

Optimal switching control design for polynomial systems: an LMI approach

Henrion

Daafouz

Claeys

2013

52nd IEEE Conference on Decision and Control

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This paper presents a linear programming approach for the optimal control of nonlinear switched systems where the control is the switching sequence. This is done by introducing modal occupation measures, which allow to relax the problem as a primal linear programming (LP) problem. Its dual linear program of HamiltonJacobi-Bellman inequalities is also characterized. The LPs are then solved numerically with a converging hierarchy of primal-dual moment-sum-of-squares (SOS) linear matrix inequalities (LMI). Because of the special structure of switched systems, we obtain a much more efficient method than could be achieved by applying standard moment/SOS LMI hierarchies for general optimal control problems.

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Section: Introductionmentioning

confidence: 99%

Optimal switching control design for polynomial systems: an LMI approach

Henrion

Daafouz

Claeys

2013

52nd IEEE Conference on Decision and Control

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“…With regard to these, the question on the determination of optimal control laws for switched systems has been widely investigated in recent years and many results are now available in the control and computer science literature. In [12,13,15], some necessary and sufficient conditions for optimality are obtained. In [2], a method for solving a hybrid optimal control problem is formulated for a two-switched system.…”

Section: Introductionmentioning

confidence: 99%

Tracking control of linear switched systems

Li¹,

Feng

Teo³

et al. 2007

ANZIAM J.

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This paper deals with the optimal tracking problem for switched systems, where the control input, the switching times and the switching index are all design variables. We propose a three-stage method for solving this problem. First, we fix the switching times and switching index sequence, which leads to a linear tracking problem, except different subsystems are defined in their respective time intervals. The optimal control and the corresponding cost function obtained depend on the switching signal. This gives rise to an optimal parameter selection problem for which the switching instants and the switching index are to be chosen optimally. In the second stage, the switching index is fixed. A reverse time transformation followed by a time scaling transform are introduced to convert this subproblem into an equivalent standard optimal parameter selection problem. The gradient formula of the cost function is derived. Then the discrete filled function is used in the third stage to search for the optimal switching index. On this basis, a computational method, which combines a gradient-based method, a local search algorithm and a filled function method, is developed for solving this problem. A numerical exampleis solved, showing the effectiveness of the proposed approach.2000 Mathematics subject classification: primary 49N90; secondary 90C11,93C95.

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“…The problem of determining optimal control laws for this class of hybrid systems has been widely investigated in the last years and many results can be found in the control and computer science literature [2,5,7,10]. Many of these works propose control procedures that are based on the discretization of state space into grids and use search methods to find optimal open-loop solutions.…”

Section: Introductionmentioning

confidence: 99%

“…Many of these works propose control procedures that are based on the discretization of state space into grids and use search methods to find optimal open-loop solutions. We also mention the contribution given by Riedinger et al in [7,8] where very general sufficient conditions for optimal control problems of switched systems are given in terms of hamiltonian function.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of switched autonomous linear systems

Giua

Seatzu

Mee

Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)

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The paper deals with the optimal control of switched piecewise linear autonomous systems, where the objective is that of minimizing a quadratic performance index over an infinite time horizon. We assume that the switching sequence and the corresponding jump matrices sequence is known, while the unknown switching times are the optimization parameters. The optimal control for this class of systems, assuming a switching sequence of finite length, takes the form of a homogeneous state feedback, i.e., it is possible to identify a homogeneous region of the state space such that an optimal switch should occur if and only if the present state belongs to this region; we show how such a region can be computed with a numerical procedure. As the number of allowed switches goes to infinity, we study the stability of the system and discuss some preliminary results related to the convergence of the state feedback law.

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An Optimal Control Approach for Hybrid Systems

Cited by 75 publications

References 14 publications

Optimal switching control design for polynomial systems: an LMI approach

Optimal switching control design for polynomial systems: an LMI approach

Tracking control of linear switched systems

Optimal control of switched autonomous linear systems

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