Global stabilizing control for a class of stochastic high-order nonlinear systems with unknown control direction

This paper considers the global stabilization for a class of stochastic high-order nonlinear systems which is in the more general form than the existing works. For details, on one hand, the considered systems accord with the high-order nonlinear system models which allow the higher system nonlinearities and is the general form of the strict-feedback systems. On the other hand, the most distinct characteristic of the systems lies in the unknown control direction, that is, the sign of the control gain is uncertain. By skillfully employing the Nussbaum function based design technique and the method of adding a power integrator, which is based on the idea of the stable domain, an effective stabilizing control design scheme is successfully presented. Under the obtained controller, it is shown that all the closed-loop system states are bounded, and especially the original system states converge to the origin, both in the sense of probability one.