Adaptive finite-time stabilisation for a class of stochastic nonlinear systems with complete unknown control coefficients

In this paper, we study the stochastic adaptive finite-time stabilisation for a class of stochastic nonlinear systems with serious uncertainties (without any known bounds), involving unknown control coefficients and uncertain nonlinear drift and diffusion terms. We first provide a finite-time control design approach that simultaneously deals with two types of uncertainties (uncertain control coefficients without any known bounds, uncertain nonlinear drift and diffusion coefficients) of stochastic nonlinear systems. To address the unknown coefficients, within the finite-time controller design procedure, we construct a Lyapunov function via a novel method. Then, we develop a stochastic adaptive finite-time controller by using the adaptive technique and the backstepping method. Furthermore, we rigorously analyse the finite-time stability in probability of the closed-loop system. Finally, to demonstrate the proposed finite-time control design method, we provide numerical simulation results of a single-link manipulator system.