relation: http://eprints.imtlucca.it/543/
title: Convex Polyhedral Invariant Sets for Closed-Loop Linear MPC Systems 
creator: Alessio, Alessandro
creator: Bemporad, Alberto
creator: Heemels, W.P.M.H.
creator: Lazar, Mircea
subject: QA Mathematics
subject: TJ Mechanical engineering and machinery
description: Given an asymptotically stabilizing linear MPC controller, this paper proposes an algorithm to construct invariant polyhedral sets for the closed-loop system. Rather than exploiting an explicit form of the MPC controller, the approach exploits a recently developed DC (Difference of Convex functions) programming technique developed by the authors to construct a polyhedral set in between two convex sets. Here, the inner convex set is any given level set V(x) les gamma of the MPC value function (implicitly defined by the quadratic programming problem associated with MPC or explicitly computed via multiparametric quadratic programming), while the outer convex set is the level set of a the value function of a modified multiparametric quadratic program (implicitly or explicitly defined). The level gamma acts as a tuning parameter for deciding the size of the polyhedral invariant containing the inner set, ranging from the origin (gamma = 0) to the maximum invariant set around the origin where the solution to the unconstrained MPC problem remains feasible, up to the whole domain of definition of the controller (possibly the whole state space Ropfn) (gamma = inf). Potential applications of the technique include reachability analysis of MPC systems and generation of constraints to supervisory decision algorithms on top of MPC loops
publisher: IEEE
date: 2006
type: Book Section
type: PeerReviewed
identifier:   Alessio, Alessandro and Bemporad, Alberto and Heemels, W.P.M.H. and Lazar, Mircea  Convex Polyhedral Invariant Sets for Closed-Loop Linear MPC Systems.   In:  Decision and Control.   IEEE, 13th-15th December 2006 , pp. 4532-4537.  ISBN 1-4244-0171-2       (2006)  
relation: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4178108&isnumber=4176993
relation: 10.1109/CDC.2006.377495