eprintid: 538
rev_number: 17
eprint_status: archive
userid: 7
dir: disk0/00/00/05/38
datestamp: 2011-07-27 08:43:43
lastmod: 2011-08-05 13:38:38
status_changed: 2011-07-27 08:43:43
type: book_section
metadata_visibility: show
contact_email: alberto.bemporad@imtlucca.it
item_issues_count: 0
creators_name: Lazar, Mircea
creators_name: Alessio, Alessandro
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
subjects: QA75
divisions: CSA
full_text_status: none
keywords: beta-contractive ellipsoidal set; ellipsoidal ones; finite termination; geometrical approach; model predictive control; nonlinear systems; polyhedral invariant set generation; polyhedral positively invariant sets; polyhedral terminal constraint sets; quadratic costs;quadratic programming; robust stability; computational geometry; nonlinear systems; quadratic programming; set theory
abstract: 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
date: 2006
date_type: published
publication: American Control Conference
publisher: IEEE
place_of_pub: 13th-15th December 2006
pagerange: 3007-3012
event_title: American Control Conference, 2006
event_location: 13th-15th December 2006
event_dates: Minneapolis
id_number: 10.1109/ACC.2006.1657178
refereed: TRUE
isbn: 1-4244-0209-3 
book_title: American Control Conference
official_url: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1657178&isnumber=34689
citation:   Lazar, Mircea and Alessio, Alessandro and Bemporad, Alberto and Heemels, W.P.M.H.  Squaring the circle: An algorithm for generating polyhedral invariant sets from ellipsoidal ones.   In:  American Control Conference.   IEEE, 13th-15th December 2006, pp. 3007-3012.  ISBN 1-4244-0209-3       (2006)