Tracking control of mechanical systems with impacts

In this paper controllers are designed such that the state trajectories of mechanical systems with impacts converge to a reference trajectory that contains impacts. The impact times of the plant will typically not coincide with those of the reference, such that the Euclidean tracking error intrinsically behaves in an unstable manner. Therefore, an alternative approach is needed and we propose to study the convergence of a non-Euclidean tracking error measure that corresponds to the intuitive notion of tracking: impact times of the plant converge to those of the reference, and the plant follows the reference away from the impacts. Sufficient conditions for asymptotic stability in terms of this tracking error are presented, and the results are illustrated with a bouncing ball example.