Stochastic Bipartite Consensus for Second-Order Multi-Agent Systems with Communication Noise and Antagonistic Information

In this paper, the bipartite consensus problem for second-order multi-agent systems with no leader, one leader and multiple leaders are investigated, where the information exchange is disturbed by measurement noise and antagonistic information. In order to attenuate the effect of communication noise, a time-varying gain c(t) is utilized and the stochastic approximation bipartite control protocol is proposed. It is given that the underlying protocol can solve the bipartite consensus problem for MASs with no leader/one leader/multiple leaders if the communication topology is strongly connected/has a spanning tree/has a spanning forest and the c(t) satisfies some mild condition. Meanwhile, for system with these three cases, a series of sufficient and necessary conditions are given. Especially, for the case with no leader, we obtain that the final state of agent is related with the initial position and initial velocity of each agent. For the case with one leader, we can get that the followers in one group can follow up the state of one leader, and the followers in another group tend to the opposite value. Additionally, for the case with multiple leaders, the containment control can be achieved where followers' states in one group can converge to the quai-convex hull of leaders' state and the ones in another group converge to the opposite convex hull. Finally, some numerical examples are given to support our new results.