relation: http://eprints.imtlucca.it/528/
title: On the stability of quadratic forms based model predictive control of constrained PWA systems
creator: Lazar, Mircea
creator: Heemels, W.P.M.H.
creator: Weiland, Siep
creator: Bemporad, Alberto
subject: QA Mathematics
subject: QA75 Electronic computers. Computer science
description: 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.
publisher: IEEE
date: 2005-06
type: Book Section
type: PeerReviewed
identifier:   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)  
relation: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1470018&isnumber=31519
relation: 10.1109/ACC.2005.1470018