Adaptive finite-time stabilization of a class of stochastic nonlinear systems

This paper studies the problem of almost surely adaptive finite-time stabilization for stochastic nonlinear systems. We prove that almost surely finite-time stabilization of stochastic nonlinear systems in triangular form can be reached by the continuous control law. The proof is based on the recently proposed almost surely finite-time stability theorem in [13]. A recursive design algorithm is developed for the construction of the adaptive controller. The adding an integrator technique is employed to construct the global almost surely finite-time stabilizer. Simulation example is given to illustrate the theoretical analysis.