Adaptive MTN Control for a Class of Stochastic Nonlinear Systems: A Novel Finite‐Time Asymptotic Tracking Control Approach

ABSTRACT This paper investigates the adaptive finite‐time asymptotic tracking control problem for a class of stochastic nonlinear systems. For the first time, an exponential decay factor is introduced into the theory of stochastic finite‐time stability, establishing a novel stochastic finite‐time asymptotic tracking criterion. Building upon this theorem, a new adaptive multi‐dimensional Taylor network (MTN) backstepping control method is proposed: During the controller design process, the same exponential decay factor is creatively incorporated. This enables rapid finite‐time convergence while guaranteeing that the tracking error asymptotically converges to zero as time approaches infinity. Utilizing Lyapunov stability theory, it is proven that the proposed control method ensures all the signals of the closed‐loop system are bounded in finite time and enables the tracking error to asymptotically converge to zero as time approaches infinity. Finally, a numerical simulation and a practical example are presented to validate the effectiveness of the proposed design method.