Dead-Zone Model-Based Adaptive Fuzzy Wavelet Control for Nonlinear Systems Including Input Saturation and Dynamic Uncertainties

In this study, the problem of adaptive fuzzy wavelet network (FWN) control is investigated for nonlinear strict-feedback systems with unknown functions, unknown virtual control gains and unknown input saturation. An adaptive FWN as an adaptive nonlinear-in-parameter approximator is proposed to represent the model of the unknown functions. Saturation nonlinearity is described by the dead-zone operator-based model which does not require the bound of the saturated input to be known. Then, a novel control scheme is designed based on the adaptive FWN, the saturation model and the dynamic surface control approach. The proposed control scheme does not require any prior knowledge about input saturation, unknown dynamics and unknown virtual control gains. It simultaneously eliminates the “explosion of complexity” and “curse of dimensionality” problems; also, the design approach avoids the controller singularity problem completely without using projection algorithm. The stability analysis is studied using Lyapunov theorem; it shows that all signals of the resulting closed-loop system are uniformly ultimately bounded and the tracking error can be made small by proper selection of the design parameters. Comparing the simulation results of the proposed scheme with other control methods demonstrates the effectiveness and superior performance of the proposed scheme.