Modular design of adaptive tracking for a class of stochastic nonlinear systems with passive identifiers

In this paper, a modular design approach of adaptive tracking is proposed for a class of 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 control module can be achieved. According to passive theorems, passive identifier module is designed. Transient performance of the system is estimated by bounds for the error state. The transient performance shows the tracking error is bounded. The hierarchy of modular design technique is concise and resulting controller is more flexible and versatile than the Lyapunov-type-based algorithms.