A Model Predictive Control Framework for Hybrid Dynamical Systems

Abstract

This paper presents a model predictive control (MPC) algorithm that asymptotically stabilizes a compact set of interest for a given hybrid dynamical system. The considered class of systems are described by a general model, which identifies the dynamics by the combination of constrained differential and difference equations. The model allows for trajectories that exhibit multiple jumps at the same time instant, or portray Zeno behavior. At every optimization time, the proposed algorithm minimizes a cost functional weighting the state and the input during both the continuous and discrete phases, and at the terminal time via a terminal cost, without discretizing the continuous dynamics. To account for the structure of time domains defining solution pairs, the minimization is performed in a manner akin to free end-time optimal control. When the terminal cost is a control Lyapunov function on the terminal constraint set, recursive feasibility and asymptotic stability of the proposed algorithm can be guaranteed. A sample-and-hold control system and a bouncing ball model are two examples reported to demonstrate the applicability and effectiveness of the proposed approach.