Finite-time stabilization for a class of stochastic nonlinear systems with stochastic inverse dynamics

In this paper, finite-time stabilization is investigated for a class of stochastic nonlinear systems with stochastic inverse dynamics. Different from the existing works about finite-time control, we give a new finite-time stability theorem for a weak solution. Under the assumption that stochastic inverse dynamics is stochastic input-to-state stable, a finite-time controller is constructively designed by the methods of backstepping and changing supply function. The closed-loop system is proved to be globally finite-time stable in probability. One simulation example is given to illustrate the efficiency of the proposed design procedure.

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