We investigate the synchronization problem of fractional-order chaotic systems with input saturation and unknown external disturbance by means of adaptive fuzzy control. An adaptive controller, accompanied with fractional adaptation law, is established, fuzzy logic systems are used to approximate the unknown nonlinear functions, and the fractional Lyapunov stability theorem is used to analyze the stability. This control method can realize the synchronization of two fractional-order chaotic or hyperchaotic systems and the synchronization error tends to zero asymptotically. Finally, we show the effectiveness of the proposed method by two simulation examples.

Stability of a class of fractional-order neural networks (FONNs) is analyzed in this paper. First, two sufficient conditions for convergence of the solution for such systems are obtained by utilizing Gronwall–Bellman lemma and Laplace transform technique. Then, according to the fractional-order Lyapunov second method and linear feedback control, the synchronization problem between two fractional-order chaotic neural networks is investigated. Finally, several numerical examples are presented to justify the feasibility of the proposed methods.

In this paper, the control of uncertain fractional-order Chua–Hartley (FOCH) chaotic systems by means of adaptive neural network backstepping control is considered. Neural network is utilized as a universal approximator to estimate the unknown nonlinear function. By using the fractional Lyapunov stability criterion and the backstepping technique, an adaptive neural network control (ANNC) method is implemented. In each backstepping step, the unknown nonlinear functions are approximated by neural networks, and a virtual control input is designed. The proposed method guarantees that all the closed-loop signals keep bounded and tracking error converges to an arbitrary small region of zero. Finally, numerical simulation is given to confirm the effectiveness and the good control performance of the proposed method.

In this paper, an adaptive neural network (NN) synchronization controller is designed for two identical strict-feedback chaotic systems (SFCSs) subject to dead-zone input. The dead-zone models together with the system uncertainties are approximated by NNs. The dynamic surface control (DSC) approach is applied in the synchronization controller design, and the traditional problem of “explosion of complexity” that usually occurs in the backstepping design can be avoided. The proposed synchronization method guarantees the synchronization errors tend to an arbitrarily small region. Finally, this paper presents two simulation examples to confirm the effectiveness and the robustness of the proposed control method.