A control Lypunov approach to predictive control of hybrid systems

S. Di Cairano, M. Lazar, A. Bemporad, W.P.M.H. Heemels

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademic

14 Citations (Scopus)

Abstract

In this paper we consider the stabilization of hybrid systems with both continuous and discrete dynamics via predictive control. To deal with the presence of discrete dynamics we adopt a "hybrid" control Lyapunov function approach, which consists of using two different functions. A Lyapunov-like function is designed to ensure finite-time convergence of the discrete state to a target value, while asymptotic stability of the continuous state is guaranteed via a classical local control Lyapunov function. We show that by combining these two functions in a proper manner it is no longer necessary that the control Lyapunov function for the continuous dynamics decreases at each time step. This leads to a significant reduction of conservativeness in contrast with classical Lyapunov based predictive control. Furthermore, the proposed approach also leads to a reduction of the horizon length needed for recursive feasibility with respect to standard predictive control approaches.
Original languageEnglish
Title of host publicationHybrid systems: computation and control ; 11th international workshop, HSCC 2008, St. Louis, MO, USA, April 22-24, 2008 ; proceedings
EditorsM. Egerstedt, B. Mishra
Place of PublicationBerlin
PublisherSpringer
Pages130-143
ISBN (Print)978-3-540-78928-4
DOIs
Publication statusPublished - 2008

Publication series

NameLecture Notes in Computer Science
Volume4981
ISSN (Print)0302-9743

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Hybrid systems
Lyapunov functions
Asymptotic stability
Stabilization

Cite this

Di Cairano, S., Lazar, M., Bemporad, A., & Heemels, W. P. M. H. (2008). A control Lypunov approach to predictive control of hybrid systems. In M. Egerstedt, & B. Mishra (Eds.), Hybrid systems: computation and control ; 11th international workshop, HSCC 2008, St. Louis, MO, USA, April 22-24, 2008 ; proceedings (pp. 130-143). (Lecture Notes in Computer Science; Vol. 4981). Berlin: Springer. https://doi.org/10.1007/978-3-540-78929-1_10
Di Cairano, S. ; Lazar, M. ; Bemporad, A. ; Heemels, W.P.M.H. / A control Lypunov approach to predictive control of hybrid systems. Hybrid systems: computation and control ; 11th international workshop, HSCC 2008, St. Louis, MO, USA, April 22-24, 2008 ; proceedings. editor / M. Egerstedt ; B. Mishra. Berlin : Springer, 2008. pp. 130-143 (Lecture Notes in Computer Science).
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Di Cairano, S, Lazar, M, Bemporad, A & Heemels, WPMH 2008, A control Lypunov approach to predictive control of hybrid systems. in M Egerstedt & B Mishra (eds), Hybrid systems: computation and control ; 11th international workshop, HSCC 2008, St. Louis, MO, USA, April 22-24, 2008 ; proceedings. Lecture Notes in Computer Science, vol. 4981, Springer, Berlin, pp. 130-143. https://doi.org/10.1007/978-3-540-78929-1_10

A control Lypunov approach to predictive control of hybrid systems. / Di Cairano, S.; Lazar, M.; Bemporad, A.; Heemels, W.P.M.H.

Hybrid systems: computation and control ; 11th international workshop, HSCC 2008, St. Louis, MO, USA, April 22-24, 2008 ; proceedings. ed. / M. Egerstedt; B. Mishra. Berlin : Springer, 2008. p. 130-143 (Lecture Notes in Computer Science; Vol. 4981).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademic

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AB - In this paper we consider the stabilization of hybrid systems with both continuous and discrete dynamics via predictive control. To deal with the presence of discrete dynamics we adopt a "hybrid" control Lyapunov function approach, which consists of using two different functions. A Lyapunov-like function is designed to ensure finite-time convergence of the discrete state to a target value, while asymptotic stability of the continuous state is guaranteed via a classical local control Lyapunov function. We show that by combining these two functions in a proper manner it is no longer necessary that the control Lyapunov function for the continuous dynamics decreases at each time step. This leads to a significant reduction of conservativeness in contrast with classical Lyapunov based predictive control. Furthermore, the proposed approach also leads to a reduction of the horizon length needed for recursive feasibility with respect to standard predictive control approaches.

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Di Cairano S, Lazar M, Bemporad A, Heemels WPMH. A control Lypunov approach to predictive control of hybrid systems. In Egerstedt M, Mishra B, editors, Hybrid systems: computation and control ; 11th international workshop, HSCC 2008, St. Louis, MO, USA, April 22-24, 2008 ; proceedings. Berlin: Springer. 2008. p. 130-143. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-540-78929-1_10