Global finite-time control for high-order stochastic nonlinear systems with multiple unknown control directions

In this article, a class of global finite-time stabilization problem for high-order stochastic nonlinear systems with multiple unknown control directions is studied. In order to solve the difficulties caused by the unknown control directions and at the same time, the system is required to converge to the origin in a limited time. Therefore, a new switching mechanism based on the Lyapunov-like function is proposed. By adding a power integral technique and utilizing sign function, a finite-time switching controller is designed. The controller parameters need to be adjusted online according to the proposed switching logic. It is rigorously proved that the designed controller can make the system state converge probabilistically to the origin in a finite-time. A simulation example shows the effectiveness of the proposed control algorithm.