Abstract
Adaptive feedback controllers based on Lyapunov's direct method for chaos control and hybrid projective synchronization (HPS) of a novel 3D chaotic system are proposed. Especially, the controller can be simplified ulteriorly into a single scalar one to achieve complete synchronization. The HPS between two nearly identical chaotic systems with unknown parameters is also studied, and adaptive parameter update laws are developed. Numerical simulations are demonstrated to verify the effectiveness of the control strategies.
Highlights
Since chaotic attractors were found by Lorentz in 1963, many chaotic systems have been constructed, such as the Lorentz system, Chen system, and Lusystem 1–8
Various types of synchronization phenomena have been found such as complete synchronization 9, 10, phase synchronization 11, partial synchronization, generalized synchronization, projective synchronization 15–17, and so forth
The controllers based on different control methods in the existing literatures, such as nonlinear feedback control 18–20, active control 21–23, adaptive control 24–26, and so forth, are mostly vectorial and they are difficult to be put into practice
Summary
Since chaotic attractors were found by Lorentz in 1963, many chaotic systems have been constructed, such as the Lorentz system, Chen system, and Lusystem 1–8. Various types of synchronization phenomena have been found such as complete synchronization 9, 10 , phase synchronization 11, , partial synchronization , generalized synchronization , projective synchronization 15–17 , and so forth They are applied in many fields, such as secure communication, neural networks, optimization of nonlinear system performance, ecological systems, modeling brain activity, system identification and pattern recognition, and so on. It can be considered as an extension of projective synchronization because complete synchronization and antisynchronization are both its special cases. We study chaos control and HPS of the new chaotic system motivated by the idea of designing simple and efficient controller for application. An adaptive nonlinear feedback vectorial controller is derived to guarantee HPS, which can degenerate into a single scalar one in the case of complete synchronization. The approaches in our paper have certain significance for reducing the cost and complexity for controller implementation
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