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

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

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review


This paper presents a new (geometrical) approach to the computation of polyhedral positively invariant sets for general (possibly discontinuous) nonlinear systems, possibly affected by disturbances. Given a beta-contractive ellipsoidal set E, the key idea is to construct a polyhedral set that lies between the ellipsoidal sets betaE 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 the computation of polyhedral terminal constraint sets for model predictive control based on quadratic costs
Originele taal-2Engels
TitelProceedings of the 25th American Control Conference(ACC2006), 14-16 June 2006, Minneapolis, Minnesota, USA
Plaats van productieMinneapolis, Minnesota, USA
ISBN van geprinte versie1-4244-0210-7
StatusGepubliceerd - 2006


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