eprintid: 528
rev_number: 14
eprint_status: archive
userid: 7
dir: disk0/00/00/05/28
datestamp: 2011-07-27 08:45:16
lastmod: 2011-08-05 13:48:46
status_changed: 2011-07-27 08:45:16
type: book_section
metadata_visibility: show
contact_email: alberto.bemporad@imtlucca.it
item_issues_count: 0
creators_name: Lazar, Mircea
creators_name: Heemels, W.P.M.H.
creators_name: Weiland, Siep
creators_name: Bemporad, Alberto
creators_id: 
creators_id: 
creators_id: 
creators_id: alberto.bemporad@imtlucca.it
title: On the stability of quadratic forms based model predictive control of constrained PWA systems
ispublished: pub
subjects: QA
subjects: QA75
divisions: CSA
full_text_status: none
keywords: Lyapunov function; Lyapunov stability; S-procedure technique; asymptotic stability; closed-loop system; constrained PWA systems; constraint set method; discrete-time PWA systems; hybrid systems; linear matrix inequalities; mixed integer quadratic programming problem; model predictive control; online optimization problem; piecewise affine systems; piecewise polyhedral positively invariant sets; quadratic cost; quadratic forms; terminal cost method; Lyapunov methods; asymptotic stability; discrete time systems; integer programming; linear matrix inequalities; piecewise polynomial techniques; predictive control; quadratic programming
abstract: In this paper we investigate the stability of discrete-time PWA systems in closed-loop with quadratic cost based Model Predictive Controllers (MPC) and we derive a priori sufficient conditions for Lyapunov asymptotic stability.
We prove that Lyapunov stability can be achieved for the
closed-loop system even though the considered Lyapunov
function and the system dynamics may be discontinuous.
The stabilization conditions are derived using a terminal
cost and constraint set method. An S-procedure technique
is employed to reduce conservativeness of the stabilization
conditions and a linear matrix inequalities set-up is developed in order to calculate the terminal cost. A new algorithm for computing piecewise polyhedral positively invariant sets for PWA systems is also presented. In this manner, the on-line optimization problem associated with MPC leads to a mixed integer quadratic programming problem, which can be solved by standard optimization tools.
date: 2005-06
publication: American Control Conference
publisher: IEEE
place_of_pub: 8th-10th June 2005
pagerange: 575-580 
event_title: American Control Conference, 2005
event_location: 8th-10th June 2005
event_dates: Portland, OR
id_number: 10.1109/ACC.2005.1470018
refereed: TRUE
isbn: 0-7803-9098-9 
book_title: American Control Conference
official_url: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1470018&isnumber=31519
citation:   Lazar, Mircea and Heemels, W.P.M.H. and Weiland, Siep and Bemporad, Alberto  On the stability of quadratic forms based model predictive control of constrained PWA systems.   In:  American Control Conference.   IEEE, 8th-10th June 2005, 575-580 .  ISBN 0-7803-9098-9       (2005)