Adaptive TOPSIS fuzzy CMAC back-stepping control system design for nonlinear systems

This paper aims to propose a more efficient control algorithm for nonlinear systems. A novel adaptive Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) fuzzy cerebellar model articulation controller (FCMAC) back-stepping control system is developed. The proposed adaptive TOPSIS FCMAC (ATFCMAC) incorporates a multi-criteria decision analysis with a fuzzy CMAC structure to determine the optimal threshold values for selecting suitable firing nodes, improving the computational efficiency, reducing the number of firing rules, and achieving good performance for nonlinear systems. A back-stepping technique is employed for the control system design. The proposed control system comprises an ATFCMAC and a robust compensator; the ATFCMAC is used to approximate an ideal controller and the robust compensator is used to reduce the influence of residual approximation error between the ideal controller and the ATFCMAC. The parameters of the proposed ATFCMAC are tuned online using the adaptation laws that are derived from a Lyapunov stability theorem, so that the stability of the control system is guaranteed. The simulation and experimental results for a Duffing–Holmes chaotic system and a magnetic ball levitation system are used to verify the effectiveness of the proposed control scheme.

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