eprintid: 474
rev_number: 10
eprint_status: archive
userid: 7
dir: disk0/00/00/04/74
datestamp: 2011-07-27 09:05:35
lastmod: 2014-07-17 12:50:21
status_changed: 2011-07-27 09:05:35
type: article
metadata_visibility: show
item_issues_count: 0
creators_name: Bemporad, Alberto
creators_name: Borrelli, Francesco
creators_name: Morari, Manfred
creators_id: alberto.bemporad@imtlucca.it
creators_id: 
creators_id: 
title: Model Predictive Control Based on Linear Programming - The Explicit Solution
ispublished: pub
subjects: TJ
divisions: CSA
full_text_status: none
keywords: Constraints; linear programming (LP); model
predictive control (MPC); multiparametric programming; piecewise linear control
abstract: We study model predictive control (MPC) schemes for discrete-time linear time-invariant systems with constraints on inputs and states, that can be formulated using a linear program (LP). In particular, we focus our attention on performance criteria based on a mixed 1 -norm, namely, 1-norm with respect to time and -norm with respect to space. First we provide a method to compute the terminal weight so that closed-loop stability is achieved. We then show that the optimal control profile is a piecewise affine and continuous function of the initial state and briefly describe the algorithm to compute it. The piecewise affine
form allows to eliminate online LP, as the computation associated with MPC becomes a simple function evaluation. Besides practical advantages, the availability of the explicit structure of the MPC controller provides an insight into the type of control action in different
regions of the state space, and highlights possible conditions of degeneracies of the LP, such as multiple optima.
date: 2002-12
publication: IEEE Transactions on Automatic Control
volume: 47
number: 12
publisher: IEEE 
pagerange: 1974-1985
id_number: 10.1109/TAC.2002.805688
refereed: TRUE
issn: 0018-9286
official_url: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1137550&isnumber=25388
citation:   Bemporad, Alberto and Borrelli, Francesco and Morari, Manfred  Model Predictive Control Based on Linear Programming - The Explicit Solution.  IEEE Transactions on Automatic Control, 47 (12).  pp. 1974-1985.  ISSN 0018-9286      (2002)