On hybrid systems and closed-loop MPC systems

A. Bemporad, W.P.M.H. Heemels, B. Schutter, de

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

5 Citations (Scopus)

Abstract

The following five classes of hybrid systems were recently proven to be equivalent: linear complementarity, extended linear complementarity, mixed logical dynamical systems, piecewise affine systems and max-min-plus-scaling systems. Some of the equivalences were obtained under additional assumptions, such as boundedness of certain system variables. In this paper, for linear or hybrid plants in closed-loop with a model predictive control (MPC) controller based on a linear model fulfilling linear constraints on input and state variables and utilizing a quadratic cost criterion, we provide a simple and direct proof that the closed-loop system is a subclass of any of the former five classes of hybrid systems. This result is of extreme importance, as it opens up the use of tools developed for the mentioned hybrid model classes, such as (robust) stability and safety analysis tools, to study closed-loop properties of MPC.
Original languageEnglish
Title of host publicationProceedings of the 40th IEEE Conference on Decision and Control, December 2001, Orlando, vol. 2
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages1645-1650
DOIs
Publication statusPublished - 2001

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