Self-organizing adaptive wavelet CMAC backstepping control system design for nonlinear chaotic systems

A novel self-organizing wavelet cerebellar model articulation controller (CMAC) is proposed. This self-organizing wavelet CMAC (SOWC) can be viewed as a generalization of a self-organizing neural network and of a conventional CMAC, and it has better generalizing, faster learning and faster recall than a self-organizing neural network and a conventional CMAC. The proposed SOWC has the advantages of structure learning and parameter learning simultaneously. The structure learning possesses the ability of on-line generation and elimination of layers to achieve optimal wavelet CMAC structure, and the parameter learning can adjust the interconnection weights of wavelet CMAC to achieve favorable approximation performance. Then a SOWC backstepping (SOWCB) control system is proposed for the nonlinear chaotic systems. This SOWCB control system is composed of a SOWC and a fuzzy compensator. The SOWC is used to mimic an ideal backstepping controller and the fuzzy compensator is designed to dispel the residual of approximation errors between the ideal backstepping controller and the SOWC. Moreover, the parameters of the SAWCB control system are on-line tuned by the derived adaptive laws in the Lyapunov sense, so that the stability of the feedback control system can be guaranteed. Finally, two application examples, a Duffing–Holmes chaotic system and a gyro chaotic system, are used to demonstrate the effectiveness of the proposed control method. The simulation results show that the proposed SAWCB control system can achieve favorable control performance and has better tracking performance than a fuzzy neural network control system and a conventional adaptive CMAC.