Synchronisation of interconnected network of nonlinear systems with Lipschitz nonlinear coupling using contraction approach

Abstract

In this work, a novel strategy for the synchronisation of nonlinear coupled networked systems is introduced. Using contraction theory, a constructive criterion for synchronisation in interconnected networked systems is proposed wherein, a systematic procedure to derive a sufficient condition is also elaborated, which ensures exponential convergence of each system. The individual systems in proposed structure of coupled network interact through integrated coupling function which satisfies Lipschitz condition. The uncoupled system nonlinearities are assumed to be restricted by an upper bound. We show using an analytical approach that nonlinear diffusive coupling in terms of Lipschitz functions provided with bounds on system states can result in suitable gains leading to synchronised behaviour of the network. The exponential convergence of each state of interconnected systems is guaranteed if and only if a sufficient condition on coupling gains and system nonlinearities is fulfilled. The efficacy of proposed approach is demonstrated by extensive simulations.

Keywords:

• Synchronisation
• contraction theory
• networked systems
• coupling configuration
• nonlinear coupling

Acknowledgments

The DST-SERB, Govt. of India and National Institute of Technology Hamirpur are appreciated by authors for supporting to carry out the research.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Yashasvi Chauhan

Yashasvi Chauhan received his Bachelor degree in electronics & communication engineering from GJU S&T, India, in 2012. Further, he received his Master in Engineering degree in signal processing & control from NIT Hamirpur, India, in 2015. During his academic journey, he actively engaged in research and had the opportunity to work on a research project in the field of synchronisation of nonlinear systems. He is currently pursuing his PhD in control theory within the field of electrical engineering at National Institute of Hamirpur, India. His research interests include Non-linear Control, Complex network, Synchronisation control and Contraction theory.

B.B. Sharma

B.B. Sharma received his B.Tech. degree in electrical engineering from Regional Engineering College Hamirpur, India, in 1997. Further, he received his Master in Engineering degree in electronics and control from BITS Pilani, India, in 1999. He received his PhD degree in electrical engineering from Indian Institute of Technology Delhi, India, in 2010. His research interests mainly include control & synchronisation of nonlinear systems, chaotic dynamics, design of nonlinear observers, etc. He has published more than 100 papers in various international journals and conferences of repute in these areas. He is Member of IEEE Control System Society, Institution of Engineers (India) and Robotic Society of India. He is presently working as an associate professor with the Department of Electrical Engineering, National Institute of Technology Hamirpur (Himachal Pradesh), India.