A new dual-mode hybrid MPC algorithm with a robust stability guarantee

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Abstract

This paper employs the Input-to-State Stability (ISS) framework to investigate the robustness of discrete-time Piece-Wise Affine (PWA) systems in closed-loop with Model Predictive Controllers (MPC), or hybrid MPC for short. We show via an example taken from literature that stabilizing hybrid MPC can generate MPC values functions that are not ISS Lyapunov functions for arbitrarily small additive disturbances. As a consequence, it is not easy to prove that nominally stabilizing hybrid MPC schemes are robust. This motivates the need to design MPC schemes for hybrid systems with an a priori robust stability guarantee. A possible solution to this problem was recently developed by the authors for a particular class of PWA systems, i.e. when the origin lies in the interior of one of the regions in the partition. The main contribution of this paper is a novel dual-mode MPC algorithm for hybrid systems with an a priori ISS guarantee. This MPC scheme is applicable to general PWA systems, i.e. when the origin may lie on the boundaries of multiple regions in the partition.

Original languageEnglish
Title of host publicationProceedings of the 2nd Second IFAC Conference on Analysis and Design of Hybrid Systems, 7-9 June 2006, Alghero, Italy
EditorsC.G. Cassandras, A. Giua, C. Seatzu, J. Zaytoon
PublisherIFAC
Pages321-328
Number of pages8
ISBN (Print)9783902661067
DOIs
Publication statusPublished - 1 Dec 2006
Event2nd IFAC Conference on Analysis and Design of Hybrid Systems, ADHS'06 - Alghero, Italy
Duration: 7 Jun 20069 Jun 2006

Conference

Conference2nd IFAC Conference on Analysis and Design of Hybrid Systems, ADHS'06
CountryItaly
CityAlghero
Period7/06/069/06/06

Fingerprint

Controllers
Hybrid systems
Robust stability
Lyapunov functions

Keywords

  • Hybrid systems
  • Predictive control
  • Robust stability

Cite this

Lazar, M., & Heemels, W. P. M. H. (2006). A new dual-mode hybrid MPC algorithm with a robust stability guarantee. In C. G. Cassandras, A. Giua, C. Seatzu, & J. Zaytoon (Eds.), Proceedings of the 2nd Second IFAC Conference on Analysis and Design of Hybrid Systems, 7-9 June 2006, Alghero, Italy (pp. 321-328). IFAC. https://doi.org/10.3182/20060607-3-IT-3902.00060, https://doi.org/10.1016/B978-008044613-4.50059-8
Lazar, M. ; Heemels, W. P.M.H. / A new dual-mode hybrid MPC algorithm with a robust stability guarantee. Proceedings of the 2nd Second IFAC Conference on Analysis and Design of Hybrid Systems, 7-9 June 2006, Alghero, Italy. editor / C.G. Cassandras ; A. Giua ; C. Seatzu ; J. Zaytoon. IFAC, 2006. pp. 321-328
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Lazar, M & Heemels, WPMH 2006, A new dual-mode hybrid MPC algorithm with a robust stability guarantee. in CG Cassandras, A Giua, C Seatzu & J Zaytoon (eds), Proceedings of the 2nd Second IFAC Conference on Analysis and Design of Hybrid Systems, 7-9 June 2006, Alghero, Italy. IFAC, pp. 321-328, 2nd IFAC Conference on Analysis and Design of Hybrid Systems, ADHS'06, Alghero, Italy, 7/06/06. https://doi.org/10.3182/20060607-3-IT-3902.00060, https://doi.org/10.1016/B978-008044613-4.50059-8

A new dual-mode hybrid MPC algorithm with a robust stability guarantee. / Lazar, M.; Heemels, W. P.M.H.

Proceedings of the 2nd Second IFAC Conference on Analysis and Design of Hybrid Systems, 7-9 June 2006, Alghero, Italy. ed. / C.G. Cassandras; A. Giua; C. Seatzu; J. Zaytoon. IFAC, 2006. p. 321-328.

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

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Lazar M, Heemels WPMH. A new dual-mode hybrid MPC algorithm with a robust stability guarantee. In Cassandras CG, Giua A, Seatzu C, Zaytoon J, editors, Proceedings of the 2nd Second IFAC Conference on Analysis and Design of Hybrid Systems, 7-9 June 2006, Alghero, Italy. IFAC. 2006. p. 321-328 https://doi.org/10.3182/20060607-3-IT-3902.00060, https://doi.org/10.1016/B978-008044613-4.50059-8