Modeling and Dynamic Surface Control of Uncertain Strict-Feedback Nonlinear Systems Using Adaptive Fuzzy Wavelet Network

This chapter proposes a new modeling and control scheme for uncertain strict-feedback nonlinear systems based on adaptive fuzzy wavelet network (FWN) and dynamic surface control (DSC) approach. It designs adaptive FWN as a nonlinear-in-parameter approximator to approximate the uncertain dynamics of the system. Then, the proposed control scheme is developed by incorporating the DSC method to the adaptive FWN-based model. Stability analysis of the proposed scheme is provided and adaptive laws are designed to learn all linear and nonlinear parameters of the network. It is proven that all the signals of the closed-loop system are uniformly ultimately bounded and the tracking error can be made arbitrary small. The proposed scheme does not require any prior knowledge about dynamics of the system and offline learning. Furthermore, it eliminates the “explosion of complexity” problems and develops accurate model of the system and simple controller. Simulation results on the numerical example and permanent magnet synchronous motor are provided to show the effectiveness of the proposed scheme.