Abstract
The adaptive hybrid function projective synchronization (AHFPS) of different chaotic systems with unknown time‐varying parameters is investigated. Based on the Lyapunov stability theory and adaptive bounding technique, the robust adaptive control law and the parameters update law are derived to make the states of two different chaotic systems asymptotically synchronized. In the control strategy, the parameters need not be known throughly if the time‐varying parameters are bounded by the product of a known function of t and an unknown constant. In order to avoid the switching in the control signal, a modified robust adaptive synchronization approach with the leakage‐like adaptation law is also proposed to guarantee the ultimately uni‐formly boundedness (UUB) of synchronization errors. The schemes are successfully applied to the hybrid function projective synchronization between the Chen system and the Lorenz system and between hyperchaotic Chen system and generalized Lorenz system. Moreover, numerical simulation results are presented to verify the effectiveness of the proposed scheme.
Highlights
Since the idea of synchronizing two identical autonomous chaotic systems under different initial conditions was first introduced in 1990 by Pecora and Carroll 1, chaos synchronization has been widely studied in physics, secure communication, chemical reactor, biological networks, and artificial neural networks
Two examples are presented to show the effectiveness of the proposed robust adaptive controllers
We have introduced the definition of AHFPS and given the AHFPS scheme of a class chaotic system with unknown time varying parameters
Summary
Since the idea of synchronizing two identical autonomous chaotic systems under different initial conditions was first introduced in 1990 by Pecora and Carroll 1 , chaos synchronization has been widely studied in physics, secure communication, chemical reactor, biological networks, and artificial neural networks. Among all kinds of chaos synchronization schemes, projective synchronization, characterized by a scaling factor that two systems synchronize proportionally, has been extensively investigated by many authors 12, 13. This is because it can obtain faster communication with its proportional feature. As compared with projective synchronization, function projective synchronization means that the drive and response systems could be synchronized up to a scaling function, which is not a constant. This characteristic could be used to get more secure communication in application to secure communications. This is because the unpredictability of the scaling function in FPS can enhance the security of communication
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