Consensus analysis of large-scale nonlinear homogeneous multi-agent formations with polynomial dynamics

TL;DR

This paper introduces an LMI-based method for proving consensus in large-scale multi-agent systems with polynomial dynamics, leveraging a generalized Kalman-Yakubovic-Popov lemma to ensure scalability.

Contribution

It develops a novel LMI-based approach inspired by linear decomposable systems theory, enabling scalable consensus analysis for polynomial multi-agent systems.

Findings

The method successfully proves consensus in academic examples.

The LMI test size remains independent of the number of agents.

Experimental validation confirms the approach's effectiveness.

Abstract

Drawing inspiration from the theory of linear "decomposable systems", we provide a method, based on linear matrix inequalities (LMIs), which makes it possible to prove the convergence (or consensus) of a set of interacting agents with polynomial dynamic. We also show that the use of a generalised version of the famous Kalman-Yakubovic-Popov lemma allows the development of an LMI test whose size does not depend on the number of agents. The method is validated experimentally on two academic examples.