Adaptive Finite-Time Control for High-Order Stochastic Nonlinear Systems with Unknown Covariance Noise

This paper is devoted to the problem of finite-time stabilization for high-order stochastic nonlinear systems driven by the noise of unknown covariance. For a class of two-dimensional stochastic nonlinear systems, the negative effect of unknown covariance can be compensated by designing an adaptive state-feedback controller with the help of adding power integrator and stochastic back-stepping technique. It is rigorously proved that the system has a unique solution and the solution is finite-time stable in probability. In addition, the above design and analysis method is applied to three-dimensional systems.