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)Full text not available from this repository.
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|
|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|
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