Stochastic fixed-time consensus problem of multi-agent systems with fixed and switching topologies

Abstract

In this paper, the fixed-time stochastic consensus problem of multi-agent systems with fixed and switching topologies is investigated. To realise the fixed-time stochastic consensus, a class of continuous non-Lipschitz protocols are designed and the effectiveness is rigorously proved. Based on the stability theory of stochastic differential equations, sufficient conditions for consensus are established. Moreover, the upper bound of the settling time is given, the influence of the algebraic connectivity of the network topologies on the convergence time is also investigated. Finally, several simulations are given to illustrate the effectiveness of the theoretical results. The simulation results show that the convergence time depends mainly on the parameters of the finite-time control term, and suitable noise can enable individuals to reach the consensus more rapidly.