eprintid: 1051
rev_number: 10
eprint_status: archive
userid: 6
dir: disk0/00/00/10/51
datestamp: 2012-01-09 14:07:35
lastmod: 2014-07-01 13:34:46
status_changed: 2012-01-09 14:07:35
type: article
metadata_visibility: show
creators_name: Bernardini, Daniele
creators_name: Bemporad, Alberto
creators_id: daniele.bernardini@imtlucca.it
creators_id: alberto.bemporad@imtlucca.it
title: Stabilizing model predictive control of stochastic constrained linear systems
ispublished: pub
subjects: QA75
subjects: TJ
divisions: CSA
full_text_status: none
keywords: Model predictive control , constrained linear systems , stochastic control 
abstract: This paper investigates stochastic stabilization procedures based on quadratic and piecewise linear Lyapunov functions for discrete-time linear systems affected by multiplicative disturbances and subject to linear constraints on inputs and states. A stochastic model predictive control (SMPC) design approach is proposed to optimize closed-loop performance while enforcing constraints. Conditions for stochastic convergence and robust constraints fulfillment of the closed-loop system are enforced by solving linear matrix inequality problems off line. Performance is optimized on line using multi-stage stochastic optimization based on enumeration of scenarios, that amounts to solving a quadratic program subject to either quadratic or linear constraints. In the latter case, an explicit form is computable to ease the implementation of the proposed SMPC law. The approach can deal with a very general class of stochastic disturbance processes with discrete probability distribution. The effectiveness of the proposed SMPC formulation is shown on a numerical example and compared to traditional MPC schemes.
date: 2012-07
date_type: published
publication: IEEE Transactions on Automatic Control 
volume: 57
number: 6
publisher: IEEE 
pagerange: 1468 -1480 
id_number: 10.1109/TAC.2011.2176429
refereed: TRUE
issn: 0018-9286
projects: This work was partially supported by the European project E-PRICE: Pricebased Control of Electrical Power Systems, FP7-IST contract no. 249096.
citation:   Bernardini, Daniele and Bemporad, Alberto  Stabilizing model predictive control of stochastic constrained linear systems.  IEEE Transactions on Automatic Control , 57 (6).  1468 -1480 .  ISSN 0018-9286      (2012)