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 | |
| 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 |
Fingerprint
Keywords
- Hybrid systems
- Predictive control
- Robust stability
Cite this
}
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
TY - GEN
T1 - A new dual-mode hybrid MPC algorithm with a robust stability guarantee
AU - Lazar, M.
AU - Heemels, W. P.M.H.
PY - 2006/12/1
Y1 - 2006/12/1
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.
AB - 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.
KW - Hybrid systems
KW - Predictive control
KW - Robust stability
UR - http://www.scopus.com/inward/record.url?scp=79960959333&partnerID=8YFLogxK
U2 - 10.3182/20060607-3-IT-3902.00060
DO - 10.3182/20060607-3-IT-3902.00060
M3 - Conference contribution
SN - 9783902661067
SP - 321
EP - 328
BT - Proceedings of the 2nd Second IFAC Conference on Analysis and Design of Hybrid Systems, 7-9 June 2006, Alghero, Italy
A2 - Cassandras, C.G.
A2 - Giua, A.
A2 - Seatzu, C.
A2 - Zaytoon, J.
PB - IFAC
ER -