Adaptive Synchronization for a Class of Fractional Order Time-delay Uncertain Chaotic Systems via Fuzzy Fractional Order Neural Network

Uncertainty and delay are common phenomena in chaotic systems, but their existence will increase the difficulty of synchronization. For the sake of actualizing synchronization of fractional order time-delay uncertain chaotic systems, we propose an adaptive fractional order fuzzy neural network synchronization scheme based on the linear matrix inequalities. A fractional order radial basis functions neural network is applied to approximate uncertainties. According to the output of the neural network, we design a general adaptive controller for fractional order time-delay uncertain chaotic systems with different topological structure. Furthermore, we propose an adaptive fractional order fuzzy neural network by introducing fuzzy rules into the network. Then the fractional order extension of the Lyapunov direct method is utilized to demonstrate the stability of the error systems under the adaptive controller. Finally, numerical simulations are conducted to verify the effectiveness of the conclusions.