Practical adaptive fuzzy tracking control for a class of perturbed nonlinear systems with backlash nonlinearity

This paper addresses the adaptive fuzzy tracking control problem for a class of perturbed nonlinear systems with backlash nonlinearity. In the proposed control scheme, fuzzy logic systems are used to approximate the unknown nonlinearity in each backstepping design, and the classic adaptive technique is employed to deal with some unknown parameters. The proposed fuzzy controller is developed by introducing some non-negative switching functions, and novel parameter adaptation learning laws are designed using the σ-modification method. It is emphasized that with the help of novel parameter adaptation laws, the high-gain phenomenon in the previous work can be avoided. In addition, by borrowing the property of the introduced non-negative functions and the inequality technique, an adaptive technique is employed to estimate the norm of the ideal weight vector such that the number of adaptation learning parameters online is reduced. By employing Barbalat's lemma, it can be proved that all the signals in the closed-loop system remain semi-globally uniformly ultimately bounded, and, especially, that the tracking error converges to an accuracy predefined a priori. Two simulation examples are provided to verify the effectiveness of the proposed control scheme.