Finite‐Time Adaptive Tracking Control for a Class of Stochastic Pure‐Feedback Nonlinear Systems With Unknown Disturbances

ABSTRACT This article first gives an improved practical finite‐time stability criterion for stochastic nonlinear systems, which offers a new idea for providing a faster convergence time. This criterion is generalized to more general stochastic nonlinear systems whose states may contain uncertainties, moreover, to the condition of Lyapunov functions including both powers less than 1 and greater than or equal to 1, which guarantees a faster convergence time while dealing with uncertainties. However, the introduction of a positive small parameter brings great difficulties to prove the provided criterion. Then, a series of new adaptive laws and controllers are devised for a class of stochastic pure‐feedback nonlinear systems with disturbances to confirm the proposed criterion. It is shown that the presented scheme allows a fast convergence time, and in the meantime can handle uncertain disturbances including internal disturbance and external disturbance.