Predictive control of hybrid systems: stability results for sub-optimal solutions

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

This article presents a novel model predictive control (MPC) scheme that achieves input-to-state stabilization of constrained discontinuous nonlinear and hybrid systems. Input-tostate stability (ISS) is guaranteed when an optimal solution of the MPC optimization problem is attained. Special attention is paid to the effect that sub-optimal solutions have on ISS of the closed-loop system. This issue is of interest as firstly, the infimum of MPC optimization problems does not have to be attained and secondly, numerical solvers usually provide only sub-optimal solutions. An explicit relation is established between the deviation of the predictive control law from the optimum (called the optimality margin) and the resulting deterioration of the ISS property of the closed-loop system (called the ISS margin).
Original languageEnglish
Title of host publicationProceedings of the 17th IFAC World Congress : 2008, Seoul, South Korea, July 6 -11,2008
EditorsHyung Suck Cho
Place of PublicationOxford
PublisherPergamon
Pages11196-11201
ISBN (Print)978-3-902661-00-5
Publication statusPublished - 2008

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Hybrid systems
System stability
Model predictive control
Closed loop systems
Deterioration
Nonlinear systems
Stabilization

Cite this

Lazar, M., & Heemels, W. P. M. H. (2008). Predictive control of hybrid systems: stability results for sub-optimal solutions. In H. S. Cho (Ed.), Proceedings of the 17th IFAC World Congress : 2008, Seoul, South Korea, July 6 -11,2008 (pp. 11196-11201). Oxford: Pergamon.
Lazar, M. ; Heemels, W.P.M.H. / Predictive control of hybrid systems: stability results for sub-optimal solutions. Proceedings of the 17th IFAC World Congress : 2008, Seoul, South Korea, July 6 -11,2008. editor / Hyung Suck Cho. Oxford : Pergamon, 2008. pp. 11196-11201
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Lazar, M & Heemels, WPMH 2008, Predictive control of hybrid systems: stability results for sub-optimal solutions. in HS Cho (ed.), Proceedings of the 17th IFAC World Congress : 2008, Seoul, South Korea, July 6 -11,2008. Pergamon, Oxford, pp. 11196-11201.

Predictive control of hybrid systems: stability results for sub-optimal solutions. / Lazar, M.; Heemels, W.P.M.H.

Proceedings of the 17th IFAC World Congress : 2008, Seoul, South Korea, July 6 -11,2008. ed. / Hyung Suck Cho. Oxford : Pergamon, 2008. p. 11196-11201.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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N2 - This article presents a novel model predictive control (MPC) scheme that achieves input-to-state stabilization of constrained discontinuous nonlinear and hybrid systems. Input-tostate stability (ISS) is guaranteed when an optimal solution of the MPC optimization problem is attained. Special attention is paid to the effect that sub-optimal solutions have on ISS of the closed-loop system. This issue is of interest as firstly, the infimum of MPC optimization problems does not have to be attained and secondly, numerical solvers usually provide only sub-optimal solutions. An explicit relation is established between the deviation of the predictive control law from the optimum (called the optimality margin) and the resulting deterioration of the ISS property of the closed-loop system (called the ISS margin).

AB - This article presents a novel model predictive control (MPC) scheme that achieves input-to-state stabilization of constrained discontinuous nonlinear and hybrid systems. Input-tostate stability (ISS) is guaranteed when an optimal solution of the MPC optimization problem is attained. Special attention is paid to the effect that sub-optimal solutions have on ISS of the closed-loop system. This issue is of interest as firstly, the infimum of MPC optimization problems does not have to be attained and secondly, numerical solvers usually provide only sub-optimal solutions. An explicit relation is established between the deviation of the predictive control law from the optimum (called the optimality margin) and the resulting deterioration of the ISS property of the closed-loop system (called the ISS margin).

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BT - Proceedings of the 17th IFAC World Congress : 2008, Seoul, South Korea, July 6 -11,2008

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Lazar M, Heemels WPMH. Predictive control of hybrid systems: stability results for sub-optimal solutions. In Cho HS, editor, Proceedings of the 17th IFAC World Congress : 2008, Seoul, South Korea, July 6 -11,2008. Oxford: Pergamon. 2008. p. 11196-11201