Modular design of adaptive controller for strict-feedback stochastic nonlinear systems with uncertain Wiener noise

In this paper, a modular approach is proposed for a class of strict-feedback stochastic nonlinear systems with uncertain 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 to guarantee that the system states are bounded and has adaptive stabilization while the covariance of Wiener noises is uncertain. According to Swapping technique, we develop two filters and convert dynamic parametric models into static ones to which the gradient update law is designed.