relation: http://eprints.imtlucca.it/479/
title: Squaring the circle: an algorithm for generating polyhedral invariant sets from ellipsoidal ones
creator: Alessio, Alessandro
creator: Lazar, Mircea
creator: Bemporad, Alberto
creator: Heemels, W.P.M.H.
subject: QA Mathematics
description: This paper presents a new (geometrical) approach to the computation of polyhedral (robustly) positively invariant (PI) sets for general (possibly discontinuous) nonlinear discrete-time systems possibly affected by disturbances. Given a β-contractive ellipsoidal set View the MathML source, the key idea is to construct a polyhedral set that lies between the ellipsoidal sets View the MathML source and View the MathML source. A proof that the resulting polyhedral set is contractive and thus, PI, is given, and a new algorithm is developed to construct the desired  polyhedral set. 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.  
publisher: Elsevier
date: 2007
type: Article
type: PeerReviewed
identifier:   Alessio, Alessandro and Lazar, Mircea and Bemporad, Alberto and Heemels, W.P.M.H.  Squaring the circle: an algorithm for generating polyhedral invariant sets from ellipsoidal ones.  Automatica, 43 (12).  pp. 2096-2103.  ISSN 0005-1098      (2007)  
relation: http://www.sciencedirect.com/science/article/pii/S0005109807003032
relation: 10.1016/j.automatica.2007.04.028