%0 Book Section
%A Di Cairano, Stefano
%A Lazar, Mircea
%A Bemporad, Alberto
%A Heemels, W.P.M.H.
%B Hybrid Systems: Computation and Control 
%D 2008
%E Egerstedt, Magnus 
%E Mishra, Bud 
%F eprints:514
%I Springer-Verlag
%P 130-143
%T A control Lyapunov approach to predictive control of hybrid systems
%U http://eprints.imtlucca.it/514/
%V 4981
%X In this paper we consider the stabilization of hybrid systems with both continuous and discrete dynamics via predictive control. To deal with the presence of discrete dynamics we adopt a “hybrid” control Lyapunov function approach, which consists of using two different functions.  A Lyapunov-like function is designed to ensure finite-time convergence of the discrete state to a target value, while asymptotic stability of the continuous state is guaranteed via a classical local control Lyapunov function. We show that by combining these two functions in a proper manner it is no longer necessary that the control Lyapunov function for the continuous dynamics decreases at each time step. This leads to a significant reduction of conservativeness in contrast with classical Lyapunov based predictive control. Furthermore, the proposed approach also leads  to a reduction of the horizon length needed for recursive feasibility with respect to standard predictive control approaches.