eprintid: 740
rev_number: 21
eprint_status: archive
userid: 37
dir: disk0/00/00/07/40
datestamp: 2011-07-29 10:52:58
lastmod: 2013-09-30 12:29:47
status_changed: 2011-07-29 10:52:58
type: book_section
metadata_visibility: show
contact_email: alberto.bemporad@imtlucca.it
item_issues_count: 0
creators_name: Rubagotti, Matteo
creators_name: Trimboli, Sergio
creators_name: Bernardini, Daniele
creators_name: Bemporad, Alberto
creators_id: 
creators_id: 
creators_id: daniele.bernardini@imtlucca.it
creators_id: alberto.bemporad@imtlucca.it
title: Stability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functions
ispublished: pub
subjects: QA
subjects: TJ
divisions: CSA
full_text_status: none
pres_type: paper
keywords: Hybrid systems stability
abstract: For piecewise affine (PWA) systems whose dynamics are only defined in a bounded and possibly non-invariant set X, this paper proposes a numerical approach to analyze the stability of the origin and to find a region of attraction. The approach relies on introducing fake dynamics outside X and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function on a larger bounded set containing X by solving a linear program. The existence of a solution proves that the origin is an asymptotically stable equilibrium of the original PWA system and determines a region of attraction contained in X. The procedure is particularly useful in practical applications for analyzing a posteriori the stability properties of approximate explicit model predictive control laws defined over a bounded set X of states, and to determine whether, for a given set of initial states, the closed-loop system evolves within the domain X where the control law is defined.
date: 2011
date_type: published
volume: 18
publisher: IFAC
event_title: 18th IFAC World Congress
event_location: Milano, Italy
event_dates: August 28 - September 2, 2011
event_type: conference
id_number: 10.3182/20110828-6-IT-1002.00539
refereed: TRUE
isbn: 978-3-902661-93-7
book_title: Proceedings of the 18th IFAC World Congress
related_url_url: http://www.ifac-papersonline.net/Detailed/49359.html
related_url_type: pub
citation:   Rubagotti, Matteo and Trimboli, Sergio and Bernardini, Daniele and Bemporad, Alberto  Stability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functions.   In:  Proceedings of the 18th IFAC World Congress.   IFAC.  ISBN 978-3-902661-93-7      (2011)