Adaptive observer design for uncertain stochastic nonlinear systems

The problem of adaptive observer design is investigated for a class of stochastic nonlinear systems with nonparametric uncertainties. Different from the existing results, the uncertainties of the systems need neither satisfy Lipschitz condition nor only contain output variable. Through the design of a nonlinear observer with an adaptive law of parameters, the system states are reconstructed. The observer has a simple structure and easy to implement. Lyapunov theorem and Itô stochastic differential theory are applied to show that the observation error convergences to the neighborhood of the origin, whose size can be adjusted by observer parameters. Finally, numerical simulation results show the effectiveness of the proposed observer.