Stability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functions

Matteo Rubagotti, Sergio Trimboli, Daniele Bernardini, Alberto Bemporad

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

10 Citations (Scopus)

Abstract

For piecewise affine (PWA) systems whose dynamics are only defined in a bounded and possibly non-invariant set χ, this paper proposes a numerical approach to analyze the stability of the origin and to find a region of attraction. The approach relies on introducing fake dynamics outside χ and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function on a larger bounded set containing χ by solving a linear program. The existence of a solution proves that the origin is an asymptotically stable equilibrium of the original PWA system and determines a region of attraction contained in χ. The procedure is particularly useful in practical applications for analyzing a posteriori the stability properties of approximate explicit model predictive control laws defined over a bounded set χ of states, and to determine whether, for a given set of initial states, the closed-loop system evolves within the domain X where the control law is defined.

Original languageEnglish
Title of host publicationProceedings of the 18th IFAC World Congress
PublisherIFAC Secretariat
Pages5712-5717
Number of pages6
Volume44
Edition1 PART 1
ISBN (Print)9783902661937
DOIs
Publication statusPublished - Jan 1 2011
Externally publishedYes

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Lyapunov functions
Invariance
Model predictive control
Closed loop systems
Dynamical systems

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Rubagotti, M., Trimboli, S., Bernardini, D., & Bemporad, A. (2011). Stability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functions. In Proceedings of the 18th IFAC World Congress (1 PART 1 ed., Vol. 44, pp. 5712-5717). IFAC Secretariat. https://doi.org/10.3182/20110828-6-IT-1002.00539

Stability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functions. / Rubagotti, Matteo; Trimboli, Sergio; Bernardini, Daniele; Bemporad, Alberto.

Proceedings of the 18th IFAC World Congress. Vol. 44 1 PART 1. ed. IFAC Secretariat, 2011. p. 5712-5717.

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

Rubagotti, M, Trimboli, S, Bernardini, D & Bemporad, A 2011, Stability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functions. in Proceedings of the 18th IFAC World Congress. 1 PART 1 edn, vol. 44, IFAC Secretariat, pp. 5712-5717. https://doi.org/10.3182/20110828-6-IT-1002.00539
Rubagotti M, Trimboli S, Bernardini D, Bemporad A. Stability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functions. In Proceedings of the 18th IFAC World Congress. 1 PART 1 ed. Vol. 44. IFAC Secretariat. 2011. p. 5712-5717 https://doi.org/10.3182/20110828-6-IT-1002.00539
Rubagotti, Matteo ; Trimboli, Sergio ; Bernardini, Daniele ; Bemporad, Alberto. / Stability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functions. Proceedings of the 18th IFAC World Congress. Vol. 44 1 PART 1. ed. IFAC Secretariat, 2011. pp. 5712-5717
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