Further results on "Robust MPC using Linear Matrix Inequalities"

M. Lazar; W.P.M.H. Heemels; D. Munoz de la Pena; T. Alamo

Further results on "Robust MPC using Linear Matrix Inequalities"

M. Lazar
, W.P.M.H. Heemels
, D. Munoz de la Pena
, T. Alamo

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

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Abstract

This paper presents a novel method for designing the terminal cost and the auxiliary control law (ACL) for robust MPC of uncertain linear systems, such that ISS is a priori guaranteed for the closed-loop system. The method is based on the solution of a set of LMIs. An explicit relation is established between the proposed method and H_infty control design. This relation shows that the LMI-based optimal solution of the H_infty synthesis problem solves the terminal cost and ACL problem in inf-sup MPC, for a particular choice of the stage cost. This result, which was somehow missing in the MPC literature, is of general interest as it connects well known linear control problems to robust MPC design.

Original language	English
Title of host publication	Proceedings of the 3rd International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control, 5-9 September 2008, Pavia, Italia
Pages	1-8
Publication status	Published - 2008
Event	3rd International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control (NMPC08) - Pavia, Italy Duration: 5 Sept 2008 → 9 Sept 2008 Conference number: 3

Workshop

Workshop	3rd International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control (NMPC08)
Abbreviated title	NMPC08
Country/Territory	Italy
City	Pavia
Period	5/09/08 → 9/09/08

Cite this

@inproceedings{247d68bf84a946a0b9d4dabae26134ce,

title = "Further results on {"}Robust MPC using Linear Matrix Inequalities{"}",

abstract = "This paper presents a novel method for designing the terminal cost and the auxiliary control law (ACL) for robust MPC of uncertain linear systems, such that ISS is a priori guaranteed for the closed-loop system. The method is based on the solution of a set of LMIs. An explicit relation is established between the proposed method and H\_infty control design. This relation shows that the LMI-based optimal solution of the H\_infty synthesis problem solves the terminal cost and ACL problem in inf-sup MPC, for a particular choice of the stage cost. This result, which was somehow missing in the MPC literature, is of general interest as it connects well known linear control problems to robust MPC design.",

author = "M. Lazar and W.P.M.H. Heemels and \{Munoz de la Pena\}, D. and T. Alamo",

year = "2008",

language = "English",

pages = "1--8",

booktitle = "Proceedings of the 3rd International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control, 5-9 September 2008, Pavia, Italia",

note = "3rd International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control (NMPC08), NMPC08 ; Conference date: 05-09-2008 Through 09-09-2008",

}

Lazar, M , Heemels, WPMH, Munoz de la Pena, D & Alamo, T 2008, Further results on "Robust MPC using Linear Matrix Inequalities". in Proceedings of the 3rd International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control, 5-9 September 2008, Pavia, Italia. pp. 1-8, 3rd International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control (NMPC08), Pavia, Italy, 5/09/08.

Further results on "Robust MPC using Linear Matrix Inequalities". / Lazar, M.; Heemels, W.P.M.H.; Munoz de la Pena, D. et al.
Proceedings of the 3rd International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control, 5-9 September 2008, Pavia, Italia. 2008. p. 1-8.

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

TY - GEN

T1 - Further results on "Robust MPC using Linear Matrix Inequalities"

AU - Lazar, M.

AU - Heemels, W.P.M.H.

AU - Munoz de la Pena, D.

AU - Alamo, T.

N1 - Conference code: 3

PY - 2008

Y1 - 2008

N2 - This paper presents a novel method for designing the terminal cost and the auxiliary control law (ACL) for robust MPC of uncertain linear systems, such that ISS is a priori guaranteed for the closed-loop system. The method is based on the solution of a set of LMIs. An explicit relation is established between the proposed method and H_infty control design. This relation shows that the LMI-based optimal solution of the H_infty synthesis problem solves the terminal cost and ACL problem in inf-sup MPC, for a particular choice of the stage cost. This result, which was somehow missing in the MPC literature, is of general interest as it connects well known linear control problems to robust MPC design.

AB - This paper presents a novel method for designing the terminal cost and the auxiliary control law (ACL) for robust MPC of uncertain linear systems, such that ISS is a priori guaranteed for the closed-loop system. The method is based on the solution of a set of LMIs. An explicit relation is established between the proposed method and H_infty control design. This relation shows that the LMI-based optimal solution of the H_infty synthesis problem solves the terminal cost and ACL problem in inf-sup MPC, for a particular choice of the stage cost. This result, which was somehow missing in the MPC literature, is of general interest as it connects well known linear control problems to robust MPC design.

M3 - Conference contribution

SP - 1

EP - 8

BT - Proceedings of the 3rd International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control, 5-9 September 2008, Pavia, Italia

T2 - 3rd International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control (NMPC08)

Y2 - 5 September 2008 through 9 September 2008

ER -

Further results on "Robust MPC using Linear Matrix Inequalities"

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