Adaptive Dynamic Surface Control for a Class of Uncertain High-order Stochastic Nonlinear Systems

To deal with the output tracking problem for a class of high-order stochastic nonlinear systems with unknown parameter vector in probability, we propose a non-smooth state-feedback dynamic surface controller. The adaptive control technology is used by the proposed controller to deal with the unknown parameter vector. And the Sigmoid function is introduced to guarantee that the derivative of the virtual controller is continuous. By means of choosing an appropriate Lyapunov function, the stability of the close-loop high-order stochastic nonlinear systems is analyzed. The main contribution lies in incorporating dynamic surface control into the non-smooth state-feedback controller design of the high-order stochastic nonlinear systems to overcome the problem of explosion of calculation. The simulation result shows that the output tracks the reference signal well in probability.