Modular Design of Adaptive Robust Controller for a Class of Stochastic Nonlinear Systems

A modular approach of the estimation-based design in the adaptive linear control systems has been extended to the adaptive robust control of strict-feedback stochastic nonlinear systems with additive standard Wiener noises and constant unknown parameters. Using Ito differentiation rule, nonlinear damping and adaptive Backstepping procedure, the disturbance-to-state stable controller of global stabilization in probability is developed which guarantees system states are bounded and has a robust stabilization. According to Swapping technique, we develop two filters and convert dynamic parametric models into static ones to which the gradient update law is designed. Transient performance of the system is estimated by bounds for the error. Results of simulation show the effectiveness of the control algorithms. The hierarchy of modular design technique is concise, and the modular design is more flexible and versatile than a Lyapunov-based algorithm.