Consensus Criterion Verification for Heterogeneous Multiagent Systems via Sum-of-Squares Programming

This article is concerned with consensus for heterogeneous multiagent systems under distributed nonlinear control protocol. Based on general Lyapunov functions beyond the quadratic form, a less conservative consensus criterion is proposed in the presence of only a directed spanning tree. Then, the consensus problem for polynomial systems can be converted into a sum-of-squares programming problem, yielding polynomial Lyapunov functions efficiently to realize the consensus criterion verification. The benefits of our method are twofold. One is the automatic verification of consensus for the heterogeneous multiagent systems, for which the widely used quadratic Lyapunov functions may not exist. The other one is the flexible generalization ability to deal with certain nonpolynomial multiagent systems. Finally, the theoretical and algorithmic developments are demonstrated on three numerical examples.

I. Introduction

Over the past decades, cooperative control of multiagent systems (MASs) has gained increasing prominence in both military and civilian domains, such as formation flying of multiple satellites [1], multirobot systems [2], wireless sensor networks [3], and unmanned aerial vehicles [4]. One of fundamental issues for the cooperative control of MASs is the consensus problem [5], [6], [7], which is to verify that all agents converge toward the nominal solution trajectory via an appropriate control protocol. Actually, consensus control protocols for MASs are designed based on the neighbors' relative information exchange among the agents, which reveals the phenomenon of animal groups in a way, such as flocking [8], swarming [9], and synchronization [10].