Infinity norms as Lyapunov functions for model predictive control of constrained PWA systems

M. Lazar, W.P.M.H. Heemels, S. Weiland, A. Bemporad, O. Pastravanu

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Abstract

In this paper we develop a priori stabilization conditions for infinity norm based hybrid MPC in the terminal cost and constraint set fashion. Closed-loop stability is achieved using infinity norm inequalities that guarantee that the value function corresponding to the MPC cost is a Lyapunov function of the controlled system. We show that Lyapunov asymptotic stability can be achieved even though the MPC value function may be discontinuous. One of the advantages of this hybrid MPC scheme is that the terminal constraint set can be directly obtained as a sublevel set of the calculated terminal cost, which is also a local piecewise linear Lyapunov function. This yields a new method to obtain positively invariant sets for PWA systems.
Original languageEnglish
Title of host publicationHybrid systems: computation and control : 8th international workshop, HSCC 2005, Zurich, Switzerland, March 9-11, 2005 ; proceedings
EditorsM. Morari, L. thiele
Place of PublicationBerlin
PublisherSpringer
Pages417-432
ISBN (Print)3-540-25108-1
DOIs
Publication statusPublished - 2005

Publication series

NameLecture Notes in Computer Science
Volume3414
ISSN (Print)0302-9743

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Model predictive control
Lyapunov functions
Costs
Asymptotic stability
Stabilization

Cite this

Lazar, M., Heemels, W. P. M. H., Weiland, S., Bemporad, A., & Pastravanu, O. (2005). Infinity norms as Lyapunov functions for model predictive control of constrained PWA systems. In M. Morari, & L. thiele (Eds.), Hybrid systems: computation and control : 8th international workshop, HSCC 2005, Zurich, Switzerland, March 9-11, 2005 ; proceedings (pp. 417-432). (Lecture Notes in Computer Science; Vol. 3414). Berlin: Springer. https://doi.org/10.1007/978-3-540-31954-2_27
Lazar, M. ; Heemels, W.P.M.H. ; Weiland, S. ; Bemporad, A. ; Pastravanu, O. / Infinity norms as Lyapunov functions for model predictive control of constrained PWA systems. Hybrid systems: computation and control : 8th international workshop, HSCC 2005, Zurich, Switzerland, March 9-11, 2005 ; proceedings. editor / M. Morari ; L. thiele. Berlin : Springer, 2005. pp. 417-432 (Lecture Notes in Computer Science).
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abstract = "In this paper we develop a priori stabilization conditions for infinity norm based hybrid MPC in the terminal cost and constraint set fashion. Closed-loop stability is achieved using infinity norm inequalities that guarantee that the value function corresponding to the MPC cost is a Lyapunov function of the controlled system. We show that Lyapunov asymptotic stability can be achieved even though the MPC value function may be discontinuous. One of the advantages of this hybrid MPC scheme is that the terminal constraint set can be directly obtained as a sublevel set of the calculated terminal cost, which is also a local piecewise linear Lyapunov function. This yields a new method to obtain positively invariant sets for PWA systems.",
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Lazar, M, Heemels, WPMH, Weiland, S, Bemporad, A & Pastravanu, O 2005, Infinity norms as Lyapunov functions for model predictive control of constrained PWA systems. in M Morari & L thiele (eds), Hybrid systems: computation and control : 8th international workshop, HSCC 2005, Zurich, Switzerland, March 9-11, 2005 ; proceedings. Lecture Notes in Computer Science, vol. 3414, Springer, Berlin, pp. 417-432. https://doi.org/10.1007/978-3-540-31954-2_27

Infinity norms as Lyapunov functions for model predictive control of constrained PWA systems. / Lazar, M.; Heemels, W.P.M.H.; Weiland, S.; Bemporad, A.; Pastravanu, O.

Hybrid systems: computation and control : 8th international workshop, HSCC 2005, Zurich, Switzerland, March 9-11, 2005 ; proceedings. ed. / M. Morari; L. thiele. Berlin : Springer, 2005. p. 417-432 (Lecture Notes in Computer Science; Vol. 3414).

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

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Lazar M, Heemels WPMH, Weiland S, Bemporad A, Pastravanu O. Infinity norms as Lyapunov functions for model predictive control of constrained PWA systems. In Morari M, thiele L, editors, Hybrid systems: computation and control : 8th international workshop, HSCC 2005, Zurich, Switzerland, March 9-11, 2005 ; proceedings. Berlin: Springer. 2005. p. 417-432. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-540-31954-2_27