Fuzzy Backstepping Control for Strict-Feedback Nonlinear Systems with Mismatched Uncertainties

Aiming at a class of strict-feedback nonlinear systems with mismatched uncertainties, an adaptive backstepping fuzzy controller design is presented. By applying backstepping design strategy and online approaching uncertainties with fuzzy approximator, the control inputs and adaptive tuning rules are derived from the Lyapunov stability theory. To deal with the problem of extreme expanded operation quantity of backstepping method, a nonlinear tracking differentiator is introduced. By choosing suitable design parameters, the developed control scheme guarantees that all the signals of the closed-loop system are uniformly ultimately bounded and the system tracking error can reach to a very small region around zero. Simulation results show the effectiveness of the proposed method.