Synchronization of Networks of Piecewise-Smooth Systems

Marco Coraggio; Pietro Delellis; S. John Hogan; Mario Di Bernardo

doi:10.1109/lcsys.2018.2845302

Synchronization of Networks of Piecewise-Smooth Systems

Marco Coraggio, Pietro Delellis, S. John Hogan, Mario Di Bernardo

Research output: Contribution to journal › Article (Academic Journal) › peer-review

4 Citations (Scopus)

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Abstract

We study convergence in networks of piecewise-smooth (PWS) systems that commonly arise in applications to model dynamical systems whose evolution is affected by macroscopic events such as switches and impacts. Existing approaches were typically oriented toward guaranteeing global bounded synchronizability, local stability of the synchronization manifold, or achieving synchronization by exerting a control action on each node. Here we start by generalizing existing results on QUAD systems to the case of PWS systems, accounting for a large variety of nonlinear coupling laws. Then, we propose that a discontinuous coupling can be used to guarantee global synchronizability of a network of N PWS agents under mild assumptions on the individual dynamics. We provide extensive numerical simulations to gain insights on larger networks.

Original language	English
Pages (from-to)	653-658
Number of pages	6
Journal	IEEE Control Systems Letters
Volume	2
Issue number	4
Early online date	7 Jun 2018
DOIs	https://doi.org/10.1109/lcsys.2018.2845302
Publication status	Published - 1 Oct 2018

Bibliographical note

Funding Information:
Manuscript received March 5, 2018; revised May 14, 2018; accepted May 29, 2018. Date of publication June 7, 2018; date of current version June 24, 2018. The work of S. J. Hogan was supported by COINOR and Compagnia di San Paolo. Recommended by Senior Editor M. Arcak. (Corresponding author: Marco Coraggio.) M. Coraggio and P. DeLellis are with the Department of Information Technology and Electrical Engineering, University of Naples Federico II, 80125 Naples, Italy (e-mail: marco.coraggio@unina.it; pietro.delellis@unina.it).

Publisher Copyright:
© 2018 IEEE.

Keywords

Switched systems
network analysis
control

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10.1109/lcsys.2018.2845302

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Accepted author manuscript, 3.72 MB

Cite this

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title = "Synchronization of Networks of Piecewise-Smooth Systems",

abstract = "We study convergence in networks of piecewise-smooth (PWS) systems that commonly arise in applications to model dynamical systems whose evolution is affected by macroscopic events such as switches and impacts. Existing approaches were typically oriented toward guaranteeing global bounded synchronizability, local stability of the synchronization manifold, or achieving synchronization by exerting a control action on each node. Here we start by generalizing existing results on QUAD systems to the case of PWS systems, accounting for a large variety of nonlinear coupling laws. Then, we propose that a discontinuous coupling can be used to guarantee global synchronizability of a network of N PWS agents under mild assumptions on the individual dynamics. We provide extensive numerical simulations to gain insights on larger networks.",

keywords = "Switched systems, network analysis, control",

author = "Marco Coraggio and Pietro Delellis and Hogan, {S. John} and {Di Bernardo}, Mario",

note = "Funding Information: Manuscript received March 5, 2018; revised May 14, 2018; accepted May 29, 2018. Date of publication June 7, 2018; date of current version June 24, 2018. The work of S. J. Hogan was supported by COINOR and Compagnia di San Paolo. Recommended by Senior Editor M. Arcak. (Corresponding author: Marco Coraggio.) M. Coraggio and P. DeLellis are with the Department of Information Technology and Electrical Engineering, University of Naples Federico II, 80125 Naples, Italy (e-mail: marco.coraggio@unina.it; pietro.delellis@unina.it). Publisher Copyright: {\textcopyright} 2018 IEEE.",

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N2 - We study convergence in networks of piecewise-smooth (PWS) systems that commonly arise in applications to model dynamical systems whose evolution is affected by macroscopic events such as switches and impacts. Existing approaches were typically oriented toward guaranteeing global bounded synchronizability, local stability of the synchronization manifold, or achieving synchronization by exerting a control action on each node. Here we start by generalizing existing results on QUAD systems to the case of PWS systems, accounting for a large variety of nonlinear coupling laws. Then, we propose that a discontinuous coupling can be used to guarantee global synchronizability of a network of N PWS agents under mild assumptions on the individual dynamics. We provide extensive numerical simulations to gain insights on larger networks.

AB - We study convergence in networks of piecewise-smooth (PWS) systems that commonly arise in applications to model dynamical systems whose evolution is affected by macroscopic events such as switches and impacts. Existing approaches were typically oriented toward guaranteeing global bounded synchronizability, local stability of the synchronization manifold, or achieving synchronization by exerting a control action on each node. Here we start by generalizing existing results on QUAD systems to the case of PWS systems, accounting for a large variety of nonlinear coupling laws. Then, we propose that a discontinuous coupling can be used to guarantee global synchronizability of a network of N PWS agents under mild assumptions on the individual dynamics. We provide extensive numerical simulations to gain insights on larger networks.

KW - Switched systems

KW - network analysis

KW - control

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DO - 10.1109/lcsys.2018.2845302

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JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

SN - 2475-1456

IS - 4

ER -

Synchronization of Networks of Piecewise-Smooth Systems

Abstract

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