Stochastic Neural Network Control for Stochastic Nonlinear Systems With Quadratic Local Asymmetric Prescribed Performance

This article presents an adaptive neural network control scheme with prescribed performance for stochastic nonlinear systems. Unlike existing adaptive stochastic control schemes that primarily utilize deterministic neural networks for approximations in complex stochastic environments, we employ stochastic neural networks to approximate the stochastic nonlinear terms, effectively resolving the "memory overflow" issue. Moreover, we propose a novel prescribed performance design method, which distinguishes itself from the previous prescribed performance control schemes by integrating a quadratic characteristic capable of suppressing transient input vibrations, along with a local asymmetric characteristic that optimize both transient output overshoot and steady-state error bias. Furthermore, the proposed control scheme is implemented within a fixed-time framework to ensure that all closed-loop systems are fixed-time bounded in probability, with the tracking error consistently within the predefined performance bounds. Simulation results validate the effectiveness of the proposed control scheme.