Infinity norms as Lyapunov functions for model predictive control of constrained PWA systems

Lazar, Mircea and Heemels, W.P.M.H. and Weiland, Siep and Bemporad, Alberto and Pastravanu, Octavian Infinity norms as Lyapunov functions for model predictive control of constrained PWA systems. In: Hybrid Systems: Computation and Control. Lecture Notes in Computer Science, 3414 . Springer-Verlag, pp. 417-432. ISBN 978-3-540-25108-8 (2005)

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Abstract

In this paper we develop a priori stabilization conditions for infinity norm based hybrid MPC in the terminal cost and constraint set fashion. Closed-loop stability is achieved using infinity norm inequalities that guarantee that the value function corresponding to the MPC cost is a Lyapunov function of the controlled system. We show that Lyapunov asymptotic stability can be achieved even though the MPC value function may be discontinuous. One of the advantages of this hybrid MPC scheme is that the terminal constraint set can be directly obtained as a sublevel set of the calculated terminal cost, which is also a local piecewise linear Lyapunov function. This yields a new method to obtain positively invariant sets for PWA systems.

Item Type: Book Section 10.1007/978-3-540-31954-2_27 H Social Sciences > HB Economic TheoryQ Science > QA MathematicsQ Science > QA Mathematics > QA75 Electronic computers. Computer scienceT Technology > TJ Mechanical engineering and machinery Computer Science and Applications Professor Alberto Bemporad 27 Jul 2011 08:47 05 Aug 2011 13:52 http://eprints.imtlucca.it/id/eprint/526