Fixed time consensus of stochastic multi-agent systems under undirected graph

Abstract

In this note, we investigate the fixed time consensus in probability for stochastic multi-agent systems under undirected graph. First, a nonlinear consensus protocol with Gaussian white noise is given, and the concept of fixed-time consensus in probability is given. Second, we prove that multi-agent systems can achieve fixed-time consensus in probability under undirected topology by using graph theory, stochastic Lyapunov theory and probability theory. Finally, a simulation example is given to verify the effectiveness of the theory results.