Nonsmooth adaptive control design for uncertain stochastic nonlinear systems

This paper investigates the problem of the global stabilization via state feedback and adaptive technique for a class of high-order stochastic nonlinear systems with more uncertainties/unknowns. First of all, two stochastic stability concepts are slightly extended to allow the systems with more than one solution. To solve the stabilization problem, a lot of substantial technical obstacles should be overcome since the presence of severe uncertainties/unknowns and stochastic noise. By introducing the appropriate control Lyapunov function and suitable adaptive updated law for an unknown design parameter, and using the method of adding a power integrator, an adaptive continuous (nonsmooth) 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.