eprintid: 493
rev_number: 17
eprint_status: archive
userid: 7
dir: disk0/00/00/04/93
datestamp: 2011-07-27 08:40:33
lastmod: 2011-08-05 13:19:18
status_changed: 2011-07-27 08:40:33
type: article
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: Stabilizing model predictive control of hybrid systems
ispublished: pub
subjects: TJ
subjects: TL
divisions: CSA
full_text_status: none
keywords: Lyapunov asymptotic stability; closed-loop; constrained piecewise affine system; discontinuous system dynamics; exponential stability; hybrid system stability; linear matrix inequality; low complexity piecewise polyhedral positively invariant sets; model predictive control; terminal constraint set; terminal cost; Lyapunov methods; asymptotic stability; closed loop systems; computational complexity; constraint theory; predictive control; sampled data systems; set theory
abstract: In this note, we investigate the stability of hybrid systems in closed-loop with model predictive controllers (MPC). A priori sufficient conditions for Lyapunov asymptotic stability and exponential stability are derived in the terminal cost and constraint set fashion, while allowing for discontinuous system dynamics and discontinuous MPC value functions. For constrained piecewise affine (PWA) systems as prediction models, we present novel techniques for computing a terminal cost and a terminal constraint set that satisfy the developed stabilization conditions. For quadratic MPC costs, these conditions translate into a linear matrix inequality while, for MPC costs based on 1, infin-norms, they are obtained as norm inequalities. New ways for calculating low complexity piecewise polyhedral positively invariant sets for PWA systems are also presented. An example illustrates the developed theory
date: 2006-11
date_type: published
publication: IEEE Transactions on Automatic Control
volume: 51
number: 11
publisher: IEEE 
pagerange: 1813-1818
id_number: 10.1109/TAC.2006.883059
refereed: TRUE
issn: 0018-9286
related_url_url: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4012327&isnumber=4012312
citation:   Lazar, Mircea and Heemels, W.P.M.H. and Weiland, Siep and Bemporad, Alberto  Stabilizing model predictive control of hybrid systems.  IEEE Transactions on Automatic Control, 51 (11).  pp. 1813-1818.  ISSN 0018-9286      (2006)