relation: http://eprints.imtlucca.it/572/
title: Optimal controllers for hybrid systems: stability and piecewise linear explicit form
creator: Bemporad, Alberto
creator: Borrelli, Francesco
creator: Morari, Manfred
subject: QA Mathematics
subject: TJ Mechanical engineering and machinery
description: 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
publisher: IEEE
date: 2000
type: Book Section
type: PeerReviewed
identifier:   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)  
relation: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=912125&isnumber=19689
relation: 10.1109/CDC.2000.912125