A Control Lyapunov Approach to Predictive Control of Hybrid Systems

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.