The Mean-square Leader-follower Two-way Convergence Of The Multi-agent System

In this paper,effects of communication noise on bipartite consensus of leader-follower multi-agent systems are considered.Multi-agent systems with leader-follower are wide-ly used in biology,engineering and so on.Agents described by continuous-time and discrete-time second-order integrator systems are studied.In order to effectively reduce the detrimental effects of communication noise,a time-varying gain function is introduced in the design of control protocol.This makes the closed-loop system a time-varying s-tochastic differential equation.Generally speaking,It is difficult to express or calculate the solution of a time-varying stochastic differential equation.With these observations,the performance of the closed-loop system is analyzed with the aid of tools from the s-tate transition matrix,Ito formula and algebraic graph theory.Necessary and sufficient conditions are given to ensure the mean-square leader-follower bipartite consensus in the presence of communication noise.It is found that for ensuring a mean square leader-follower bipartite consensus the weakest communication conditions are communication topology among agents having a spanning tree and being structurally balanced.