eprintid: 472
rev_number: 9
eprint_status: archive
userid: 7
dir: disk0/00/00/04/72
datestamp: 2011-07-27 09:02:43
lastmod: 2011-08-04 07:29:08
status_changed: 2011-07-27 09:02:43
type: article
metadata_visibility: show
contact_email: alberto.bemporad@imtlucca.it
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: Min-max control of constrained uncertain discrete-time linear systems
ispublished: pub
subjects: QA75
subjects: TJ
divisions: CSA
full_text_status: none
keywords: additive norm-bounded input disturbances; constrained uncertain discrete-time linear systems; constraints; continuous piecewise affine function; finite-horizon robust optimal control law; min-max control formulation; multiparametric linear programs; optimal control law; polyhedral parametric uncertainties; receding horizon scheme; robust optimal feedback controller; robustness; state feedback controllers; state vector; state-space matrices; constraint theory; control system synthesis; discrete time systems; linear programming; linear systems; minimax techniques; minimisation; optimal control; piecewise constant techniques; robust control; state feedback; state-space methods; uncertain systems
abstract: For discrete-time uncertain linear systems with constraints on inputs and states, we develop an approach to determine state feedback controllers based on a min-max control formulation. Robustness is achieved against additive norm-bounded input disturbances and/or polyhedral parametric uncertainties in the state-space matrices. We show that the finite-horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs. When the optimal control law is implemented in a receding horizon scheme, only a piecewise affine function needs to be evaluated on line at each time step. The technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state-space.
date: 2003-09
date_type: published
publication: IEEE Transactions on Automatic Control 
volume: 48
number: 9
publisher: IEEE
pagerange: 1600-1606
id_number: 10.1109/TAC.2003.816984
refereed: TRUE
issn: 0018-9286
official_url: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1231253&isnumber=27582
citation:   Bemporad, Alberto and Borrelli, Francesco and Morari, Manfred  Min-max control of constrained uncertain discrete-time linear systems.  IEEE Transactions on Automatic Control , 48 (9).  pp. 1600-1606.  ISSN 0018-9286      (2003)