eprintid: 572
rev_number: 10
eprint_status: archive
userid: 7
dir: disk0/00/00/05/72
datestamp: 2011-07-27 09:11:18
lastmod: 2014-07-17 12:17:22
status_changed: 2011-07-27 09:11:17
type: book_section
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: Optimal controllers for hybrid systems: stability and piecewise linear explicit form
ispublished: pub
subjects: QA
subjects: TJ
divisions: CSA
full_text_status: none
keywords: closed-loop stability; heat exchange system; hybrid systems; input trajectories; linear function evaluation; mixed logical dynamical framework; model predictive controller; multiparametric mixed-integer linear program; piecewise affine systems; piecewise linear optimal controllers; stabilizing controller; tracking error; weighted 1/∞-norm; closed loop systems; control system synthesis; discrete time systems; heat exchangers; integer programming; linear programming; optimal control; predictive control; stability
abstract: We propose a procedure for synthesizing piecewise linear optimal controllers for hybrid systems and investigate conditions for closed-loop stability. Hybrid systems are modeled in discrete-time within the mixed logical dynamical framework, or, equivalently, as piecewise affine systems. A stabilizing controller is obtained by designing a model predictive controller, which is based on the minimization of a weighted 1/∞-norm of the tracking error and the input trajectories over a finite horizon. The control law is obtained by solving a mixed-integer linear program (MILP) which depends on the current state. Although efficient branch and bound algorithms exist to solve MILPs, these are known to be NP-hard problems, which may prevent their online solution if the sampling-time is too small for the available computation power. Rather than solving the MILP online, we propose a different approach where all the computation is moved off line, by solving a multiparametric MILP. As the resulting control law is piecewise affine, online computation is drastically reduced to a simple linear function evaluation. An example of piecewise linear optimal control of a heat exchange system shows the potential of the method
date: 2000
date_type: published
publication: Proc. 39th IEEE Conf. on Decision and Control
volume: 2
publisher: IEEE
place_of_pub: Sydney, Australia December, 2000
pagerange: 1810-1815
event_dates: Sydney, Australia
id_number: 10.1109/CDC.2000.912125
refereed: TRUE
isbn: 0-7803-6638-7 
book_title: Decision and Control Conference
official_url: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=912125&isnumber=19689
citation:   Bemporad, Alberto and Borrelli, Francesco and Morari, Manfred  Optimal controllers for hybrid systems: stability and piecewise linear explicit form.   In:  Decision and Control Conference.   IEEE, Sydney, Australia December, 2000, pp. 1810-1815.  ISBN 0-7803-6638-7       (2000)