Bemporad, Alberto and Heemels, W.P.M.H. and De Schutter, Bart
*On hybrid systems and closed-loop MPC systems.*
IEEE Transactions on Automatic Control, 47 (5).
pp. 863-869.
ISSN 0018-9286
(2002)

## Abstract

The following five classes of hybrid systems were recently proven to be equivalent: linear complementarity, extended linear complementarity, mixed logical dynamical systems, piecewise affine systems and max-min-plus-scaling systems. Some of the equivalences were obtained under additional assumptions, such as boundedness of certain system variables. In this paper, for linear or hybrid plants in closed-loop with a model predictive control (MPC)controller based on a linear model fulfilling linear constraints on input and state variables and utilizing a quadratic cost criterion, we provide a simple and direct proof that the closed-loop system is a subclass of any of the former five classes of hybrid systems. This result is of extreme importance, as it opens up the use of tools developed for the mentioned hybrid model classes, such as (robust) stability and safety analysis tools, to study closed-loop properties of MPC

Item Type: | Article |
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Identification Number: | 10.1109/TAC.2002.1000287 |

Uncontrolled Keywords: | bounded system variables; closed-loop model predictive control systems; equivalent systems; hybrid systems; input variables; linear complementarity; linear constraints; linear model; linear plants; max-min-plus-scaling systems; mixed analogue/logical systems; mixed continuous/discrete systems;mixed logical dynamical systems;piecewise affine systems; quadratic cost criterion; robust stability; safety analysis tools; state variables; closed loop systems; discrete systems; linear systems; predictive control; safety; stability |

Subjects: | Q Science > QA Mathematics > QA75 Electronic computers. Computer science T Technology > TJ Mechanical engineering and machinery |

Research Area: | Computer Science and Applications |

Depositing User: | Professor Alberto Bemporad |

Date Deposited: | 27 Jul 2011 09:05 |

Last Modified: | 17 Jul 2014 12:52 |

URI: | http://eprints.imtlucca.it/id/eprint/473 |

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