Controlled synchronization of mechanical systems with a unilateral constraint
Michael Baumann (ETH Zürich)
J. J Benjamin Biemond (Katholieke Universiteit Leuven)
Remco I. Leine (University of Stuttgart)
Nathan van de Wouw (University of Minnesota, Eindhoven University of Technology, TU Delft - Team Bart De Schutter)
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Abstract
This paper addresses the controlled synchronization problem of mechanical systems subjected to a geometric unilateral constraint as well as the design of a switching coupling law to obtain synchronization. To define the synchronization problem, we propose a distance function induced by the quotient metric, which is based on an equivalence relation using the impact map. A Lyapunov function is constructed to investigate the synchronization problem for two identical one-dimensional mechanical systems. Sufficient conditions for the individual systems and their controlled interaction are provided under which synchronization can be ensured. We present a (coupling) control law which ensures global synchronization, also in the presence of grazing trajectories and accumulation points (Zeno behavior). The results are illustrated using a numerical example.