Adaptive Finite-time Stabilization of Weak Solutions for a Class of Stochastic Nonlinear Systems with Parametric Uncertainty

In this paper, the finite-time stabilization for a class of stochastic nonlinear systems with parametric uncertainty is studied under the framework of weak solutions. A Lyapunov function is constructed by the method of adding a power integrator and a finite-time controller is constructively designed. It is proved that the closed-loop system has a global weak solution, states and control input of the closed-loop system reach the origin in a finite time and the parameter estimate is bounded with probability one. Finally, a numerical simulation is given to illustrate the efficiency of the proposed design procedure.