Distributed Robust Estimation and Adaptive Control for Cooperative Games in T-S Fuzzy Systems

This paper proposes a unified framework that deeply integrates distributed estimation, cooperative control, and evolutionary game for Takagi-Sugeno (T-S) fuzzy systems. Unlike previous studies that treat estimation, control. and game problems separately and neglect external disturbances, we design a distributed fuzzy observer with a neighbor-estimation interaction mechanism to mitigate disturbances. Specifically, an adaptive control law based on neighbors' state deviations is introduced, which enables online gain updates and dynamic compensation of cooperative states. These components are embedded in a unified framework, where neighbors’ relative states serve as game variables for online optimization in continuous action spaces. By using the Lyapunov function, we strictly prove the uniformly ultimately bounded of the designed observer and the T-S fuzzy system. Finally, two typical game models, the prisoner's dilemma and the stag hunt game, are used to demonstrate the effectiveness and robustness of the designed distributed observer and controller.