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Further Results on “Robust MPC Using Linear Matrix Inequalities”

  • M. Lazar
  • W. P. M. H. Heemels
  • D. Muñoz de la Peña
  • T. Alamo
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 384)

Abstract

This paper presents a novelmethod 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 \(\mathcal{H}_\infty\) control design. This relation shows that the LMI-based optimal solution of the \(\mathcal{H}_\infty\) 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.

Keywords

robust model predictive control (MPC) linear matrix inequalities (LMIs) \(\mathcal{H}_\infty\) control input-to-state stability (ISS) 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • M. Lazar
    • 1
  • W. P. M. H. Heemels
    • 1
  • D. Muñoz de la Peña
    • 2
  • T. Alamo
    • 2
  1. 1.Eindhoven Univ. of TechnologyEindhovenThe Netherlands
  2. 2.Dept. de Ingeniería de Sistemas y AutomáticaUniv. of SevilleSevilleSpain

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