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.
|Title of host publication||Hybrid systems: computation and control ; 11th international workshop, HSCC 2008, St. Louis, MO, USA, April 22-24, 2008 ; proceedings|
|Editors||M. Egerstedt, B. Mishra|
|Place of Publication||Berlin|
|Publication status||Published - 2008|
|Name||Lecture Notes in Computer Science|