Novel Hybrid Intelligent Backstepping Controller for Chaotic Systems

This paper proposes a novel hybrid intelligent backstepping controller (HIBC) for control of uncertain nonlinear chaotic systems. The novel HIBC uses a hybrid Fuzzy System-Wavelet Neural Network identifier (FS-WNN) to identify the system unknown dynamics. The hybrid FS-WNN identifier is a combination of a Fuzzy System approximator (FS) and a Wavelet Neural Network approximator (WNN). Each approximator approximates the unknown functions of the system separately. Then, the different approximations of the same function are combined using modulation technique. Since the hybrid FS-WNN uses wavelet neural networks and fuzzy systems, its approximation accuracy and generalization capability are superior to those of conventional individual wavelet neural network and fuzzy system for system identification. The adaptation laws of the control system are obtained using Lyapunov's method to guarantee the asymptotic stability of the closed loop system. The proposed HIBC is applied to control a chaotic uncertain nonlinear system. Simulation results prove that the proposed HIBC can achieve a superior tracking performance by incorporation of WNN identifier, FS identifier, adaptive backstepping control technique, and Lyapunov's theory of stability. A comparison of the HIBC performance with further models in literature is given to highlight the efficiency of the proposed control scheme.