Controlled synchronization of mechanical systems with a unilateral constraint

Michael Baumann, J. J Benjamin Biemond, Remco I. Leine, Nathan van de Wouw

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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.

Original languageEnglish
Title of host publicationIFAC-PapersOnLine
Subtitle of host publicationProceedings 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2016)
EditorsAndrew Teel
Place of PublicationLaxenburg, Austria
Publication statusPublished - 2016
Event10th IFAC Symposium on Nonlinear Control Systems - Monterey, United States
Duration: 23 Aug 201625 Aug 2016
Conference number: 10

Publication series



Conference10th IFAC Symposium on Nonlinear Control Systems
Abbreviated titleNOLCOS 2016
CountryUnited States


  • hybrid systems
  • Lyapunov stability
  • measure differential inclusions
  • Synchronization
  • unilateral constraints

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