Lazar, Mircea and Heemels, W.P.M.H. and Weiland, Siep and Bemporad, Alberto
*On the stability of quadratic forms based model predictive control of constrained PWA systems.*
In:
American Control Conference.
IEEE, 8th-10th June 2005, 575-580 .
ISBN 0-7803-9098-9
(2005)

## Abstract

In this paper we investigate the stability of discrete-time PWA systems in closed-loop with quadratic cost based Model Predictive Controllers (MPC) and we derive a priori sufficient conditions for Lyapunov asymptotic stability. We prove that Lyapunov stability can be achieved for the closed-loop system even though the considered Lyapunov function and the system dynamics may be discontinuous. The stabilization conditions are derived using a terminal cost and constraint set method. An S-procedure technique is employed to reduce conservativeness of the stabilization conditions and a linear matrix inequalities set-up is developed in order to calculate the terminal cost. A new algorithm for computing piecewise polyhedral positively invariant sets for PWA systems is also presented. In this manner, the on-line optimization problem associated with MPC leads to a mixed integer quadratic programming problem, which can be solved by standard optimization tools.

Item Type: | Book Section |
---|---|

Identification Number: | 10.1109/ACC.2005.1470018 |

Uncontrolled Keywords: | Lyapunov function; Lyapunov stability; S-procedure technique; asymptotic stability; closed-loop system; constrained PWA systems; constraint set method; discrete-time PWA systems; hybrid systems; linear matrix inequalities; mixed integer quadratic programming problem; model predictive control; online optimization problem; piecewise affine systems; piecewise polyhedral positively invariant sets; quadratic cost; quadratic forms; terminal cost method; Lyapunov methods; asymptotic stability; discrete time systems; integer programming; linear matrix inequalities; piecewise polynomial techniques; predictive control; quadratic programming |

Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science |

Research Area: | Computer Science and Applications |

Depositing User: | Professor Alberto Bemporad |

Date Deposited: | 27 Jul 2011 08:45 |

Last Modified: | 05 Aug 2011 13:48 |

URI: | http://eprints.imtlucca.it/id/eprint/528 |

### Actions (login required)

Edit Item |