eprintid: 2253
rev_number: 8
eprint_status: archive
userid: 6
dir: disk0/00/00/22/53
datestamp: 2014-07-08 14:21:55
lastmod: 2014-07-08 14:21:55
status_changed: 2014-07-08 14:21:55
type: conference_item
metadata_visibility: show
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: Stability of hybrid model predictive control
ispublished: unpub
subjects: TL
divisions: CSA
full_text_status: public
pres_type: paper
keywords: Hybrid systems, Piecewise Affine systems, Model Predictive Control, Lyapunov stability.
abstract: In this paper we investigate the stability of hybrid systems in closed-loop with Model Predictive
Controllers (MPC) and we derive a priori sufficient conditions for Lyapunov asymptotic stability and
exponential stability. A general theory is presented which proves that Lyapunov stability is achieved for
both terminal cost and constraint set and terminal equality constraint hybrid MPC, even though the
considered Lyapunov function and the system dynamics may be discontinuous. For particular choices
of MPC criteria and constrained Piecewise Affine (PWA) systems as the prediction models we develop
novel algorithms for computing the terminal cost and the terminal constraint set. For a quadratic MPC
cost, the stabilization conditions translate into a linear matrix inequality while, for an 1-norm based
MPC cost, they are obtained as 1-norm inequalities. It is shown that by using 1-norms, the terminal
constraint set is automatically obtained as a polyhedron or a finite union of polyhedra by taking a
sublevel set of the calculated terminal cost function. New algorithms are developed for calculating
polyhedral or piecewise polyhedral positively invariant sets for PWA systems. In this manner, the on-line
optimization problem leads to a mixed integer quadratic programming problem or to a mixed integer
linear programming problem, which can be solved by standard optimization tools. Several examples
illustrate the effectiveness of the developed methodology.
date: 2004-12
pagerange: 1-40
event_title: 43rd IEEE Conference on Decision and Control
event_location: Atlantis, Paradise Island, Bahamas
event_dates: December 14-17, 2004 
event_type: conference
refereed: TRUE
citation:   Lazar, Mircea and Heemels, W.P.M.H. and Weiland, Siep and Bemporad, Alberto  Stability of hybrid model predictive control.  In: 43rd IEEE Conference on Decision and Control, December 14-17, 2004 , Atlantis, Paradise Island, Bahamas pp. 1-40.      (Unpublished)   (2004)  
document_url: http://eprints.imtlucca.it/2253/1/MLazarIEEE_2005draft.pdf