Adaptive fixed-time control for stochastic nonlinear systems with unknown covariance noise

This article investigates the issue of adaptive fixed-time control for stochastic nonlinear systems with unknown covariance noise. First, we derive a significant corollary regarding fixed-time stability in stochastic nonlinear systems. This corollary provides the minimum bound for the settling time, which is a crucial parameter in assessing the system's performance and stability. The adaptive control strategy is used to compensate the detrimental effect caused by unknown covariance noise. Then, in order to ensure the fixed-time stability of the closed-loop system, an adaptive state-feedback controller is constructed by utilizing backstepping method and the adding a power integrator technique. Moreover, the settling time estimate provided by the proposed control law is less conservative, meaning it allows for a more accurate prediction of the actual settling time compared to more traditional approaches. Finally, the simulation results are presented to verify the correctness of our theoretical results proposed in this paper.