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 proceedingConference contributionAcademicpeer-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 languageEnglish
Title of host publicationProceedings of the 3rd International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control, 5-9 September 2008, Pavia, Italia
Pages1-8
Publication statusPublished - 2008
Event3rd International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control (NMPC08) - Pavia, Italy
Duration: 5 Sep 20089 Sep 2008
Conference number: 3

Workshop

Workshop3rd International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control (NMPC08)
Abbreviated titleNMPC08
CountryItaly
CityPavia
Period5/09/089/09/08

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Linear matrix inequalities
Costs
Closed loop systems
Linear systems

Cite this

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

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 proceedingConference contributionAcademicpeer-review

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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.

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Lazar M, Heemels WPMH, Munoz de la Pena D, Alamo T. 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. 2008. p. 1-8