Modular design of adaptive tracking of stochastic nonlinear systems based on generalized Least-Square algorithm

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. According to the Swapping technique, filters were designed to convert dynamic parametric models into static models. In view of unknown covariance, we choose generalized Least-Square algorithms and give the generalized Least-Square update laws, then discuss the estimate of the covariance.