Controlled synchronization of mechanical systems with a unilateral constraint

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

doi:10.1016/j.ifacol.2016.10.188

Controlled synchronization of mechanical systems with a unilateral constraint

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

Team Bart De Schutter

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

1 Citation (Scopus)

57 Downloads (Pure)

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.

Original language	English
Title of host publication	IFAC-PapersOnLine
Subtitle of host publication	Proceedings 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2016)
Editors	Andrew Teel
Place of Publication	Laxenburg, Austria
Publisher	Elsevier
Pages	339-344
DOIs	https://doi.org/10.1016/j.ifacol.2016.10.188
Publication status	Published - 2016
Event	10th IFAC Symposium on Nonlinear Control Systems - Monterey, United States Duration: 23 Aug 2016 → 25 Aug 2016 Conference number: 10

Publication series

Name	IFAC-PapersOnLine
Number	18
Volume	49

Conference

Conference	10th IFAC Symposium on Nonlinear Control Systems
Abbreviated title	NOLCOS 2016
Country/Territory	United States
City	Monterey
Period	23/08/16 → 25/08/16

Keywords

hybrid systems
Lyapunov stability
measure differential inclusions
Synchronization
unilateral constraints

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10.1016/j.ifacol.2016.10.188

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Baumann, M., Biemond, J. J. B., Leine, R. I., & van de Wouw, N. (2016). Controlled synchronization of mechanical systems with a unilateral constraint. In A. Teel (Ed.), IFAC-PapersOnLine: Proceedings 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2016) (pp. 339-344). (IFAC-PapersOnLine; Vol. 49, No. 18). Elsevier. https://doi.org/10.1016/j.ifacol.2016.10.188

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title = "Controlled synchronization of mechanical systems with a unilateral constraint",

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.",

keywords = "hybrid systems, Lyapunov stability, measure differential inclusions, Synchronization, unilateral constraints",

author = "Michael Baumann and Biemond, {J. J Benjamin} and Leine, {Remco I.} and {van de Wouw}, Nathan",

year = "2016",

doi = "10.1016/j.ifacol.2016.10.188",

language = "English",

series = "IFAC-PapersOnLine",

publisher = "Elsevier",

number = "18",

pages = "339--344",

editor = "Teel, {Andrew }",

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note = "10th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2016 ; Conference date: 23-08-2016 Through 25-08-2016",

}

Baumann, M, Biemond, JJB, Leine, RI & van de Wouw, N 2016, Controlled synchronization of mechanical systems with a unilateral constraint. in A Teel (ed.), IFAC-PapersOnLine: Proceedings 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2016). IFAC-PapersOnLine, no. 18, vol. 49, Elsevier, Laxenburg, Austria, pp. 339-344, 10th IFAC Symposium on Nonlinear Control Systems, Monterey, United States, 23/08/16. https://doi.org/10.1016/j.ifacol.2016.10.188

Controlled synchronization of mechanical systems with a unilateral constraint. / Baumann, Michael; Biemond, J. J Benjamin; Leine, Remco I. et al.
IFAC-PapersOnLine: Proceedings 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2016). ed. / Andrew Teel. Laxenburg, Austria: Elsevier, 2016. p. 339-344 (IFAC-PapersOnLine; Vol. 49, No. 18).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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N2 - 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.

AB - 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.

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KW - Lyapunov stability

KW - measure differential inclusions

KW - Synchronization

KW - unilateral constraints

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Controlled synchronization of mechanical systems with a unilateral constraint

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