Tracking of a Bouncing Ball in a Planar Billiard Through Continuous-Time Approximations

Abstract

The main goal of this paper is to design a state feedback control that makes a point mass track a non-Zeno reference trajectory in a planar billiard. This objective is achieved by first determining a continuous-time dynamical model, whose trajectories approximate the solutions of the hybrid system. Hence, a state feedback that makes the hybrid system track a reference trajectory of the continuous-time one is proposed. Finally, these two techniques are combined in order to find a state feedback that achieves tracking of the trajectories of the unforced system. Examples are reported all throughout the paper to illustrate the theoretical results.