Nonsmooth Adaptive Control Design for a Large Class of Uncertain High-Order Stochastic Nonlinear Systems

This paper investigates the problem of the global stabilization via partial-state feedback and adaptive technique for a class of high-order stochastic nonlinear systems with more uncertainties/unknowns and stochastic zero dynamics. First of all, two stochastic stability concepts are slightly extended to allow the systems with more than one solution. To solve the problem, a lot of substantial technical difficulties should be overcome since the presence of severe uncertainties/unknowns, unmeasurable zero dynamics, and stochastic noise. By introducing the suitable adaptive updated law for an unknown design parameter and appropriate control Lyapunov function, and by using the method of adding a power integrator, an adaptive continuous (nonsmooth) partial-state feedback controller without overparameterization is successfully designed, which guarantees that the closed-loop states are bounded and the original system states eventually converge to zero, both with probability one. A simulation example is provided to illustrate the effectiveness of the proposed approach.