Distributed Discontinuous Coupling for Convergence in Networks of Heterogeneous Nonlinear Systems

TL;DR

This paper introduces a distributed discontinuous coupling method to synchronize heterogeneous nonlinear systems in networks, providing analytical estimates for coupling gains and validating results through simulations.

Contribution

It presents a novel distributed discontinuous coupling protocol that guarantees convergence and synchronization in networks of non-identical nonlinear systems, with theoretical and numerical validation.

Findings

Synchronization achieved with appropriate coupling gains

Analytical estimates for critical coupling gains derived

Numerical simulations confirm theoretical predictions

Abstract

Synchronization is a crucial phenomenon in many natural and artificial complex network systems. Applications include neuronal networks, formation control and coordination in robotics, and frequency synchronization in electrical power grids. In this paper, we propose the use of a distributed discontinuous coupling protocol to achieve convergence and synchronization in networks of non-identical nonlinear dynamical systems. We show that the synchronous dynamics is a solution to the average of the nodes' vector fields, and derive analytical estimates of the critical coupling gains required to achieve convergence. Numerical simulations are used to illustrate and validate the theoretical results.