Squaring the circle : an algorithm for generating polyhedral invariant sets from ellipsoidal ones

A. Alessio, M. Lazar, A. Bemporad, W.P.M.H. Heemels

Research output: Contribution to journalArticleAcademicpeer-review

20 Citations (Scopus)

Abstract

This paper presents a new (geometrical) approach to the computation of polyhedral positively invariant sets for general (possibly discontinuous) nonlinear discrete-time systems possibly affected by disturbances. Given a b-contractive ellipsoidal set E, the key idea is to construct a polyhedral set that lies between the ellipsoidal sets bE and E. A proof that the resulting polyhedral set is positively invariant (and contractive under an additional assumption) is given, and a new algorithm is developed to construct the desired polyhedral set. An advantage of the proposed method is that the problem of computing polyhedral invariant sets is formulated as a number of Quadratic Programming (QP) problems. The number of QP problems is guaranteed to be finite and therefore, the algorithm has finite termination. An important application of the proposed algorithm is thecomputation of polyhedral terminal constraint sets for model predictive control based on quadratic costs.
Original languageEnglish
Pages (from-to)2096-2103
Number of pages8
JournalAutomatica
Volume43
Issue number12
DOIs
Publication statusPublished - 2007

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