Consensus of Multi-Agent Systems With Piecewise Continuous Time-Varying Topology

Wangui Yuan,Guangjie Han

doi:10.1109/access.2019.2927992

Abstract

This paper studies the consensus of multi-agent systems with piecewise continuous time-varying topology. The agents are assumed to have identical first-order linear dynamics, which their underlying communication topology is piecewise continuous time-varying. In the case of undirected time-varying communication topology, the consensus of the multi-agent system depends on the connectivity of its limit topology, and the states of all agents converge to the mean of their initial states. However, the consensus depends on the absolute integrability of the elements in the difference matrix between the Laplacian matrix and the limit matrix when the communication topology is directed and connected. Several simulation examples are presented to validate the proposed theories.

Highlights

The research on the behavior of biological groups has become a hot research topic in the world
We mainly study the consensus of linear multi-agent systems with piecewise continuous time-varying topology
DIRECTED TIME-VARYING COMMUNICATION NETWORK TOPOLOGY In this subsection, we mainly study the sufficient condition of consensus when the network topology is directed time-varying of the system (3)

Summary

INTRODUCTION

The research on the behavior of biological groups has become a hot research topic in the world. The theorem 1 points out that the consensus of multi-agent system, with undirected piecewise continuous (or continuous) time-varying communication topology, tends to be stable depends on whether their asymptotically stable topological graphs are connected or not. Theorem 2: Let L(t), the Laplacian matrix of the multi-agent system (3) with directed time-varying topology, be continuous or piecewise continuous in time and satisfies (4). Theorem 2 shows that the consensus is affected by both the connectivity of the limit communication topology and the Absolute Integrability of the Laplace error matrix O(t) for first-order linear multi-agent systems with time-varying and asymptotically stable communication topology. For the first-order linear multi-agent system with directed time-varying communication topology, the consensus is determined by the connectivity of the limit topology and the convergence speed of the communication topology graph

SIMULATION RESEARCH

SIMULATION OF THE SYSTEM WITH UNDIRECTED

SUMMARIZATION