Modular design of adaptive tracking for a class of stochastic nonlinear systems

In this paper, a modular design approach of adaptive tracking is proposed for parameter-strict-feedback stochastic nonlinear systems with standard Wiener noises and constant unknown parameters. Both the adaptive backstepping procedure and input-to-state stable (ISS) controller of global stabilization in probability are designed separately to ensure the output-feedback tracking can be achieved. According to swapping technique, we develop two filters and convert dynamic parametric models into a static one to which the gradient update law is chosen. The transient performance shows the tracking error is bounded.