Guaranteed-cost consensus for multiagent networks with Lipschitz nonlinear dynamics and switching topologies

TL;DR

This paper develops a method for achieving guaranteed-cost consensus in high-order nonlinear multi-agent networks with switching topologies, using a novel transformation and linearization techniques.

Contribution

It introduces a new approach to decompose and linearize nonlinear multi-agent dynamics for guaranteed-cost consensus under switching topologies.

Findings

The proposed method guarantees consensus with minimized cost.

The approach effectively handles Lipschitz nonlinear dynamics.

Numerical simulations validate the theoretical results.

Abstract

Guaranteed-cost consensus for high-order nonlinear multi-agent networks with switching topologies is investigated. By constructing a time-varying nonsingular matrix with a specific structure, the whole dynamics of multi-agent networks is decomposed into the consensus and disagreement parts with nonlinear terms, which is the key challenge to be dealt with. An explicit expression of the consensus dynamics, which contains the nonlinear term, is given and its initial state is determined. Furthermore, by the structure property of the time-varying nonsingular transformation matrix and the Lipschitz condition, the impacts of the nonlinear term on the disagreement dynamics are linearized and the gain matrix of the consensus protocol is determined on the basis of the Riccati equation. Moreover, an approach to minimize the guaranteed cost is given in terms of linear matrix inequalities. Finally, the numerical simulation is shown to demonstrate the effectiveness of theoretical results.