Formation Control with Communication Noises in Second-order Multi-agent Systems

Formation control problem has been studied in this paper, where the additive communication noises are considered in the position and velocity vectors. First, the proposed problem is transformed into the convergence problem of infinite products of general stochastic matrices. Based on the convex analysis theory, several convex polytopes have been constructed in order to analyze this problem. Then, a sufficient condition is derived to guarantee that the position with communication noises of agents can approach the desired position as well as the velocity with communication noises of agents. Finally, an example is presented to show the effectiveness of the result.