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

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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.