Abstract
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.
Highlights
Chaos phenomena, which have attracted increasing attention of scholars from many fields, intensively exist in many actual nonlinear systems
A number of methods have been developed for the chaotic systems, for example, pinning control [10], adaptive control [11, 12], sliding mode control (SMC) [13, 14], backstepping control, and many others
In [11], adaptive fuzzy controller was designed for fractional-order chaotic systems with dead-zone
Summary
Chaos phenomena, which have attracted increasing attention of scholars from many fields, intensively exist in many actual nonlinear systems. In [11], adaptive fuzzy controller was designed for fractional-order chaotic systems with dead-zone. Base on the adaptive fuzzy backstepping technique, the control of uncertain fractional-order nonlinear systems was investigated in [15]. The system uncertainties are approximated by NNs; secondly, based on the fractional Lyapunov stability theory, a fractional adaptation law that ensures that the states of a system converge to a small region of zero is designed; the NN backstepping controller is implemented step by step. The main contribution of the proposed method includes the following: (1) Adaptive NN control together with backstepping control method is proposed for fractional-order chaotic systems, and the prior knowledge of the system model is not needed. Remark 3 In this paper, backstepping control approach is used This is a technique of designing stabilizing controls for systems with triangular form. The aforementioned control methods can not be used as a recursive algorithm
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