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

M. Lazar; W. P.M.H. Heemels

doi:10.3182/20060607-3-IT-3902.00060

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

M. Lazar, W. P.M.H. Heemels

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

1 Citation (Scopus)

2 Downloads (Pure)

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 language	English
Title of host publication	Proceedings of the 2nd Second IFAC Conference on Analysis and Design of Hybrid Systems, 7-9 June 2006, Alghero, Italy
Editors	C.G. Cassandras, A. Giua, C. Seatzu, J. Zaytoon
Publisher	IFAC
Pages	321-328
Number of pages	8
ISBN (Print)	9783902661067
DOIs	https://doi.org/10.3182/20060607-3-IT-3902.00060 https://doi.org/10.1016/B978-008044613-4.50059-8
Publication status	Published - 1 Dec 2006
Event	2nd IFAC Conference on Analysis and Design of Hybrid Systems, ADHS'06 - Alghero, Italy Duration: 7 Jun 2006 → 9 Jun 2006

Conference

Conference	2nd IFAC Conference on Analysis and Design of Hybrid Systems, ADHS'06
Country	Italy
City	Alghero
Period	7/06/06 → 9/06/06

Keywords

Hybrid systems
Predictive control
Robust stability

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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

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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.",

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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 proceeding › Conference contribution › Academic › peer-review

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N2 - 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.

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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