Agreement for networked multi-agent systems with noisy communications

In this paper, a distributed consensus protocol is proposed for discrete-time single-integral multi-agent systems with communication noises under general fixed directed topologies. The time-varying control gains satisfying the stochastic approximation conditions are introduced to attenuate noises, thus the closed-loop multi-agent system is intrinsically a linear time-varying stochastic difference system. Then the mean square consensus convergence analysis is developed based on the Lyapunov technique, and the construction of the Lyapunov function especially does not require the balanced network topology condition assumed for the existence of quadratic Lyapunov function. It is proved that the state of each agent converges in mean square to a common random variable whose mathematical expectation is the weighted average of agents´ initial state values; meanwhile, the variance of the random variable is bounded. The proposed protocol can be applicable to more general multi-agent networks, particularly when the bidirectional and/or balanced information communications are not required.