Adaptive Control for a Class of Mismatched Uncertain System

Combining backstepping with variable structure control (VSC) scheme, an adaptive neural controller design for a class of mismatched uncertain nonlinear system with inputs containing sector nonlinearity and dead zone is presented. By applying online approximating uncertainties with fully tuned radial basis function (RBF) neural networks (NNs), the adaptive tuning rules are derived from the Lyapunov stability theory. At the same time, the nonlinear tracking differentiator is introduced to deal with the problem of extreme expanded operation quantity of backstepping. By theoretical analysis, the closed-loop control system is proved to be uniformly ultimately bounded, and the proposed controller can be applied to the systems either with or without series nonlinearity and/or dead zone in the input. Simulation results demonstrate the good tracking performance and robustness of the approach.