Robust adaptive backstepping controller for a class of nonlinear cascade systems via fuzzy neural networks

In this paper, a robust adaptive backstepping control scheme using fuzzy neural networks, called FNN-ABC, is proposed for a class of nonlinear uncertain systems with cascade structure. Each subsystem is in the form of lower triangular and non-affine systems which contains of external disturbance, uncertainties, or parameters variations. By the backstepping approach, a fuzzy neural network (FNN) based robust adaptive controller is designed in a step by step manner for each subsystem. Two kinds of FNN systems are used to estimate the subsystems’ unknown functions. According to the FNNs’ estimations, the FNN-ABC control input can be generated by Lyapunov approach such that system output follows the desired trajectory. To enhance the control performance (or FNNs’ approximation accuracy), a Taylor expansion method are adopted to derive the update laws of FNNs’ antecedent-part parameters. Based on the Lyapunov approach, the adaptive laws of FNNs’ parameters and stability analysis of closed-loop system are obtained. Finally, the proposed FNN-ABC is applied to the tracking control of a single-link flexible-joint robot. A simulation study is proposed to illustrate the performances of our approach.