In this paper, a consensus problem is investigated for a linear multi-agent system with communication noises and cooperative-competitive interactions. The interaction network associated with the multi-agent system is modeled by a signed graph. A mean square bipartite consensus problem is formulated for the multi-agent system. Under some mild assumptions, distributed dynamic control laws are proposed for all agents by using a stochastic-approximation approach and some algebraic Riccati equations. The mean square consensus error is analyzed for the closed-loop system. A simulation example is presented to demonstrate the effectiveness of the proposed control strategy.
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