Adaptive Backstepping Control and Application for Strict-Feedback Nonlinear Systems with Mismatched Uncertainties

Aiming at a class of strict-feedback nonlinear systems with mismatched uncertainties, an adaptive backstepping neural controller design is presented. By applying backstepping design strategy and online approaching uncertainties with fully tuned radial basis function (RBF) neural networks, the adaptive tuning rules are derived from the Lyapunov stability theory. To deal with the problem of extremely expanded operation quantity of backstepping method, a nonlinear tracking differentiator is introduced. The developed control scheme guarantees that all the signals of the closed-loop system are uniform ultimate boundedness. Experiment of an electro-hydraulic shaker shows the effectiveness of the proposed method.