Modular design of adaptive tracking of stochastic nonlinear systems based on passive identifiers

The estimation-base modular design was applied for the adaptive tracking problems for a class of stochastic nonlinear in the form of parametric-strict-feedback driven by Wiener noises of unknown covariance. We achieve a complete controller-identifier separation by employing Lyapunov function and using the ISS controller with strong parametric robustness properties. For the noise of unknown covariance, we apply the adaptive design. According to the passive theorems, a passive identifier module is designed to guarantee the boundedness of the state error. Therefore, the result that the tracking error converges to a small residual set in probability was obtained.