Mask-based privacy-preserving adaptive bipartite fuzzy consensus control for stochastic nonlinear multi-agent systems...

This paper studies an adaptive bipartite fuzzy consensus problem with privacy preservation in stochastic nonlinear multi-agent systems (SNMASs) under Markovian switching topologies. To handle unknown nonlinearities and protect sensitive information, a novel observer-based control strategy is proposed, in which adaptive fuzzy logic systems (FLSs) are employed to approximate unknown nonlinear functions and a vanishing affine mask function is designed to ensure the privacy of the agents' initial states. A continuous-time Markov process governs stochastic topology changes, improving network robustness and adaptability. Theoretical analysis demonstrates that all signals of the closed-loop system are uniformly ultimately bounded in the mean-square sense, and practical bipartite consensus is achieved in the face of stochastic disturbances and nonlinearities. Notably, the proposed method is further extended to structurally unbalanced signed graphs by constructing a virtually balanced graph through pinning-type compensations, enabling the consensus protocol to operate directly on the original structurally unbalanced network while preserving convergence guarantees. Finally, the effectiveness of the proposed theoretical approach is validated through numerical simulations.