Leader-Following Mean Square Scaled Bipartite Consensus for Second-Order Multi-Agent Systems with Communication Noise and Antagonistic Information

In this paper, we study the leader-follower scaled bipartite consensus problem for second-order multi-agent systems with communication noise and antagonistic information. In order to reduce the negative impact of communication noise on information transmission, we design a stochastic approximation protocol with time-varying gain c(t). Compared with the existing consensus results with communication noise, the challenge is that the introduction of time-varying gain leads to the failure of the Lyapunov method. A state decomposition method is used to solve this problem, and the necessary and sufficient conditions for the convergence of the multi-agent system under constant velocity and zero velocity are given. Finally, the results are validated by two simulations.