Regional input-to-state stability of min-max model predicitive control

D.M. Raimondo; D. Limon; M. Lazar; D. Magni; E.F. Camacho

Regional input-to-state stability of min-max model predicitive control

D.M. Raimondo, D. Limon, M. Lazar, D. Magni, E.F. Camacho

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

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Abstract

The objective of this paper is, on the base of existing results, to provide a general framework for synthesizing min-max MPC schemes with an a priori robust stability guarantee for nonlinear constrained systems. Using regional input-to-state stability, it is proven that the standard min-max approach can only guarantee practical stability. This is due to the choice of the stage cost. In order to avoid this problem, two different solutions have been considered: the first one is based on a particular design of the stage cost of the performance index, while the second one is based on a dual-mode strategy. It is shown that under fairly mild assumptions both controllers guarantee input-to-state stability.

Original language	English
Title of host publication	Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), 21-24 August 2007, Pretoria, South Africa
Editors	X. Xia, F. Camisani-Calzolari
Place of Publication	Oxford
Publisher	Pergamon
Pages	116-121
ISBN (Print)	978-1-605-60751-1
Publication status	Published - 2007
Event	conference; 7th IFAC Symposium on Nonlinear Control Systems; 2007-08-22; 2007-08-24 - Duration: 22 Aug 2007 → 24 Aug 2007

Conference

Conference	conference; 7th IFAC Symposium on Nonlinear Control Systems; 2007-08-22; 2007-08-24
Period	22/08/07 → 24/08/07
Other	7th IFAC Symposium on Nonlinear Control Systems

Cite this

@inproceedings{97463dc3561e47e58f4d444b10595b4f,

title = "Regional input-to-state stability of min-max model predicitive control",

abstract = "The objective of this paper is, on the base of existing results, to provide a general framework for synthesizing min-max MPC schemes with an a priori robust stability guarantee for nonlinear constrained systems. Using regional input-to-state stability, it is proven that the standard min-max approach can only guarantee practical stability. This is due to the choice of the stage cost. In order to avoid this problem, two different solutions have been considered: the first one is based on a particular design of the stage cost of the performance index, while the second one is based on a dual-mode strategy. It is shown that under fairly mild assumptions both controllers guarantee input-to-state stability.",

author = "D.M. Raimondo and D. Limon and M. Lazar and D. Magni and E.F. Camacho",

year = "2007",

language = "English",

isbn = "978-1-605-60751-1",

pages = "116--121",

editor = "X. Xia and F. Camisani-Calzolari",

booktitle = "Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), 21-24 August 2007, Pretoria, South Africa",

publisher = "Pergamon",

note = "conference; 7th IFAC Symposium on Nonlinear Control Systems; 2007-08-22; 2007-08-24 ; Conference date: 22-08-2007 Through 24-08-2007",

}

Raimondo, DM, Limon, D, Lazar, M, Magni, D & Camacho, EF 2007, Regional input-to-state stability of min-max model predicitive control. in X Xia & F Camisani-Calzolari (eds), Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), 21-24 August 2007, Pretoria, South Africa. Pergamon, Oxford, pp. 116-121, conference; 7th IFAC Symposium on Nonlinear Control Systems; 2007-08-22; 2007-08-24, 22/08/07.

Regional input-to-state stability of min-max model predicitive control. / Raimondo, D.M.; Limon, D.; Lazar, M. et al.
Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), 21-24 August 2007, Pretoria, South Africa. ed. / X. Xia; F. Camisani-Calzolari. Oxford: Pergamon, 2007. p. 116-121.

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

TY - GEN

T1 - Regional input-to-state stability of min-max model predicitive control

AU - Raimondo, D.M.

AU - Limon, D.

AU - Lazar, M.

AU - Magni, D.

AU - Camacho, E.F.

PY - 2007

Y1 - 2007

N2 - The objective of this paper is, on the base of existing results, to provide a general framework for synthesizing min-max MPC schemes with an a priori robust stability guarantee for nonlinear constrained systems. Using regional input-to-state stability, it is proven that the standard min-max approach can only guarantee practical stability. This is due to the choice of the stage cost. In order to avoid this problem, two different solutions have been considered: the first one is based on a particular design of the stage cost of the performance index, while the second one is based on a dual-mode strategy. It is shown that under fairly mild assumptions both controllers guarantee input-to-state stability.

AB - The objective of this paper is, on the base of existing results, to provide a general framework for synthesizing min-max MPC schemes with an a priori robust stability guarantee for nonlinear constrained systems. Using regional input-to-state stability, it is proven that the standard min-max approach can only guarantee practical stability. This is due to the choice of the stage cost. In order to avoid this problem, two different solutions have been considered: the first one is based on a particular design of the stage cost of the performance index, while the second one is based on a dual-mode strategy. It is shown that under fairly mild assumptions both controllers guarantee input-to-state stability.

M3 - Conference contribution

SN - 978-1-605-60751-1

SP - 116

EP - 121

BT - Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), 21-24 August 2007, Pretoria, South Africa

A2 - Xia, X.

A2 - Camisani-Calzolari, F.

PB - Pergamon

CY - Oxford

T2 - conference; 7th IFAC Symposium on Nonlinear Control Systems; 2007-08-22; 2007-08-24

Y2 - 22 August 2007 through 24 August 2007

ER -

Regional input-to-state stability of min-max model predicitive control

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