Bipartite Containment of Multi-Leader Multi-Agent Systems With Antagonistic Information and Measurement Noise

This paper is concerned with the mean square and almost sure bipartite containment of multi-leader multi-agent systems with antagonistic information and measurement noise. By designing the modified time-varying bipartite containment protocol, the weak conditions are investigated under signed graph. For the case with additive noise, the sufficient and necessary conditions for stochastic bipartite containment are obtained by employing the semidecoupled method, the law of the iterated logarithm for martingales, and the variation of constants formula. For the case with multiplicative noise, a Lyapunov-based method and semimartingale convergence theorem are used to obtain the sufficient conditions for stochastic bipartite containment. This paper shows that the states of followers will finally converge to the deterministic constant formed by leaders' states. The effectiveness of the theoretical results is verified through numerical simulations.