A Mean Square Average Consensus Protocol for Discrete-Time Double-Integrator Multi-Agent Systems with Communication Noises

摘要

An average consensus protocol is proposed for discrete-time double-integrator multi-agent systems with communication noises under fixed topologies. The proposed consensus protocol is composed of two parts: the agent's own state feedback and the relative states between the agent and its neighbor agents. Due to the existence of communication noises, the relative states cannot be obtained accurately. To attenuate the noise effect, a time-varying consensus gain a(k) is applied to the relative states in the proposed protocol. Hence, the closed-loop dynamics of multi-agent systems is a linear stochastic difference equation with variable coefficients. Fortunately, the state transition matrix of this stochastic system can be solved, and the dynamical behavior of linear multi-agent systems can therefore be determined. It is proved that the proposed protocol is able to solve the mean square average consensus problem if and only if the topology graph is connected; and the time-varying gain a(k) satisfies the stochastic-approximation type conditions (Omission)。