Lazar, Mircea and Heemels, W.P.M.H. and Weiland, Siep and Bemporad, Alberto
*Stabilizing model predictive control of hybrid systems.*
IEEE Transactions on Automatic Control, 51 (11).
pp. 1813-1818.
ISSN 0018-9286
(2006)

## Abstract

In this note, we investigate the stability of hybrid systems in closed-loop with model predictive controllers (MPC). A priori sufficient conditions for Lyapunov asymptotic stability and exponential stability are derived in the terminal cost and constraint set fashion, while allowing for discontinuous system dynamics and discontinuous MPC value functions. For constrained piecewise affine (PWA) systems as prediction models, we present novel techniques for computing a terminal cost and a terminal constraint set that satisfy the developed stabilization conditions. For quadratic MPC costs, these conditions translate into a linear matrix inequality while, for MPC costs based on 1, infin-norms, they are obtained as norm inequalities. New ways for calculating low complexity piecewise polyhedral positively invariant sets for PWA systems are also presented. An example illustrates the developed theory

Item Type: | Article |
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Identification Number: | 10.1109/TAC.2006.883059 |

Uncontrolled Keywords: | Lyapunov asymptotic stability; closed-loop; constrained piecewise affine system; discontinuous system dynamics; exponential stability; hybrid system stability; linear matrix inequality; low complexity piecewise polyhedral positively invariant sets; model predictive control; terminal constraint set; terminal cost; Lyapunov methods; asymptotic stability; closed loop systems; computational complexity; constraint theory; predictive control; sampled data systems; set theory |

Subjects: | T Technology > TJ Mechanical engineering and machinery T Technology > TL Motor vehicles. Aeronautics. Astronautics |

Research Area: | Computer Science and Applications |

Depositing User: | Professor Alberto Bemporad |

Date Deposited: | 27 Jul 2011 08:40 |

Last Modified: | 05 Aug 2011 13:19 |

URI: | http://eprints.imtlucca.it/id/eprint/493 |

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