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On the stability of quadratic forms based model predictive control of constrained PWA systems

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)

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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

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