Research on Bipartite Synchronization of Multi-Agent Systems in Complex Networks Under Distributed Control Strategies

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Abstract
This paper investigates the bipartite synchronization problem in complex networks of agents with three-dimensional nonlinear dynamics. To address the challenges posed by system nonlinearity, heterogeneous node behaviors, and the requirement of fully distributed control, a novel nonlinear saturated controller based on the hyperbolic tangent function is proposed and compared with the traditional linear proportional controller. Furthermore, a unified modeling approach based on the Kronecker product is introduced to compactly represent the global error dynamics, enabling rigorous Lyapunov-based stability analysis and explicit derivation of sufficient conditions for global asymptotic bipartite synchronization. Comparative numerical simulations demonstrate that, compared with the linear controller, the proposed nonlinear controller achieves faster convergence rates, higher synchronization accuracy, and stronger robustness against initial disturbances. The proposed framework is theoretically reliable, practically implementable, and scalable, with potential applications in multi-UAV coordination, distributed sensing, and edge intelligence systems.

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