Further results on stabilization for a class of stochastic high-order nonlinear systems with unknown control directions
This paper concerns the global stabilization for a class of stochastic high-order nonlinear systems which admit more general system form than those in the existing works. For details, except for the serious system nonlinearities which show that the considered system is the general of the strict-feedback systems, the most distinct feature of the systems is exhibited by the unknown control directions, that is, all the control coefficients of the virtual and actual control have unknown signs. By skillfully employing the Nussbaum function, and applying the method of adding a power integrator, an effective regulation control scheme is successfully provided for the considered systems. In particular, the presented controller can guarantee 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.