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)

## 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

Item Type: | Book Section |
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Identification Number: | 10.1109/CDC.2000.912125 |

Uncontrolled 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 |

Subjects: | Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery |

Research Area: | Computer Science and Applications |

Depositing User: | Professor Alberto Bemporad |

Date Deposited: | 27 Jul 2011 09:11 |

Last Modified: | 17 Jul 2014 12:17 |

URI: | http://eprints.imtlucca.it/id/eprint/572 |

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