relation: http://eprints.imtlucca.it/740/
title: Stability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functions
creator: Rubagotti, Matteo
creator: Trimboli, Sergio
creator: Bernardini, Daniele
creator: Bemporad, Alberto
subject: QA Mathematics
subject: TJ Mechanical engineering and machinery
description: 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.
publisher: IFAC
date: 2011
type: Book Section
type: PeerReviewed
identifier:   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)  
relation: 10.3182/20110828-6-IT-1002.00539