Consensus problems with arbitrary sign-preserving nonlinearities

TL;DR

This paper investigates consensus in multi-agent systems with nonlinear, possibly discontinuous functions on directed graphs, providing conditions for convergence and using port-Hamiltonian methods for certain cases.

Contribution

It offers new sufficient conditions for consensus with nonlinear, discontinuous functions and applies port-Hamiltonian techniques for strongly connected graphs with continuous functions.

Findings

Sufficient conditions for consensus based on graph topology and nonlinear functions

Convergence proof for systems with continuous functions using port-Hamiltonian formulation

Applicability to directed, strongly connected graphs

Abstract

This paper studies consensus problems for multi-agent systems defined on directed graphs where the consensus dynamics involves nonlinear and discontinuous functions. Sufficient conditions, involving the nonlinear functions and the topology of the underlying graph, for the agents to converge to consensus are provided. For a special case, namely the multi-agent system defined on a strongly connected graph with continuous functions, we show the convergence by using a port-Hamiltonian formulation.