Adaptive Neural Network‐Based Fixed‐Time Control of Stochastic High‐Order Nonlinear Systems With Unmodeled Dynamics and Multiple Time‐Varying Delays

ABSTRACT For stochastic nonlinear high‐order systems with unmodeled dynamics together with time‐varying both state and input delays, this paper investigates the fixed‐time tracking control problem for the first time. First, an adaptive neural network‐based controller is designed by integrating the neural network method with adaptive backstepping to solve algebraic loop issues under non‐strict feedback. An improved Lyapunov–Krasovskii function is constructed to compensate for time‐varying state delays, while dynamic and compensation signals are used to handle unmodeled dynamics and input delays, respectively. Then, based on the semi‐global practical fixed‐time stability theory, the boundedness of all signals in the closed‐loop system is proven, demonstrating that the convergence time is independent on system initial values. Finally, simulation examples are given and demonstrate the effectiveness of the devised control scheme.