eprintid: 479
rev_number: 13
eprint_status: archive
userid: 7
dir: disk0/00/00/04/79
datestamp: 2011-07-27 08:36:50
lastmod: 2011-08-05 13:03:30
status_changed: 2011-07-27 08:36:50
type: article
metadata_visibility: show
contact_email: alberto.bemporad@imtlucca.it
item_issues_count: 0
creators_name: Alessio, Alessandro
creators_name: Lazar, Mircea
creators_name: Bemporad, Alberto
creators_name: Heemels, W.P.M.H.
creators_id: 
creators_id: 
creators_id: alberto.bemporad@imtlucca.it
creators_id: 
title: Squaring the circle: an algorithm for generating polyhedral invariant sets from ellipsoidal ones
ispublished: pub
subjects: QA
divisions: CSA
full_text_status: none
keywords: Positively invariant sets; Contractive sets; Model predictive control; Stability; Robust stability
abstract: 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.

date: 2007
date_type: published
publication: Automatica
volume: 43
number: 12
publisher: Elsevier
pagerange: 2096-2103
id_number: 10.1016/j.automatica.2007.04.028 
refereed: TRUE
issn: 0005-1098
official_url: http://www.sciencedirect.com/science/article/pii/S0005109807003032
citation:   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)