Synchronization Control Strategy Of Fractional-order Chaotic System And Its Application In Secure Communication

With the continuous development of science and technology,the frequent occurrence of information security incidents has caused the public to pay more attention to secure communication technology.Traditional communication methods have problems such as confidentiality loopholes,capacity limitations,inefficient attack protection and high equipment costs.Chaotic systems are highly random,aperiodic and unpredictable.The high-capacity dynamic storage capacity and low equipment costs of the new chaotic communication technology show obvious technical advantages and broad application prospects.In this paper,the novel complete synchronization and generalized synchronization control strategy is proposed for various uncertain fractional-order chaotic systems,and the research on secure communication application is conducted.The main work is as follows:Firstly,based on the analysis of various type of sliding mode synchronization control for the gyroscope system,an improved adaptive non-singular terminal sliding mode synchronization control strategy is designed for the n dimension fractional-order nonautonomous chaotic system with external disturbance.This part gives the dynamic modeling of the gyro system and design of various sliding mode variable structure synchronization control,including adaptive terminal sliding mode synchronization control,adaptive fast non-singular terminal sliding mode synchronization control and fractional-order proportional differential sliding mode synchronization control.Then,an improved adaptive fractional-order nonsingular terminal sliding mode synchronization control strategy is proposed and stability analysis is performed.Under external disturbance,two-dimensional fractional-order Duffing oscillator system and three-dimensional fractional-order Genesio-Tesi system are selected for simulation and compared with fractional-order PID controller,fractional-order PD sliding mode controller and adaptive terminal sliding mode controller.Compared with the existing synchronization control method,the proposed method has higher error accuracy and faster convergence speed,and the control is smooth.Secondly,for the four-dimensional hyperchaotic fractional-order Rabinovich system,generalized synchronization is achieved using the active control method,and for the timedelayed fractional-order chaotic system,the lag generalized synchronization control strategy based on fractional-order extended state observer is designed to achieve generalized synchronization.The characteristics of the new four-dimensional hyperchaotic Rabinovich system are analyzed,and the active control method is used to complete the design of the generalized synchronization control strategy.In order to improve the performance of the active control method,a novel lag generalized synchronization control strategy based on the fractional-order extended state observer is designed for the time-delayed fractional-order chaotic system in the presence of transmission delay.The effective generalized synchronization for the time-delayed fractional-order chaotic system is completed and unknown dynamics of the system can be estimated.The lag generalized synchronization control strategy can be extended to other synchronization types and various complex fractional-order chaotic systems.After completing the design of the lag generalized synchronization control strategy,the samestructure time-delayed fractional-order systems and different-structure time-delayed fractionalorder systems with external disturbance are selected for simulation.The comparison with the active control method can verify the effectiveness of the novel lag generalized synchronization control strategy.Compared with the existing method,the complicated calculation of dynamic error is avoided,and good synchronization performance,anti-interference performance and fast response speed are guaranteed when facing external disturbance.Thirdly,the existing chaotic synchronization mainly aims at the synchronization behavior of two fractional-order chaotic systems,this section designs a generalized switched synchronization control strategy for multiple time-delayed fractional-order chaotic systems.Considering the effect of fractional order and time delay on chaotic behavior,the system analysis of fractional-order time-delayed financial system,fractional-order time-delayed Chen system and fractional-order time-delayed Liu system is carried out.The appropriate fractionalorder and time-delay are selected.Based on the design of the switch bit,scale factor and projection coefficient,a generalized switched synchronization control scheme for three timedelayed fractional-order chaotic systems is proposed.The validity of the control scheme is verified by Matlab simulation.Finally,based on the proposed novel complete synchronization control strategy of the fractional-order chaotic systems,a dual-channel three-time chaotic secure communication scheme is designed.The proposed communication scheme includes two channels,one channel is used to achieve the synchronization of the drive system and the response system,and the other channel is used to transmit useful information.At the transmitting end,the state information of the fractional-order chaotic system and the designed key are used to perform three-time signal modulation on the useful information source.At the receiving end,the mixednoise signal is decrypted by the state information of fractional-order chaotic system obtained by chaotic synchronization and protocol cryptography.Compared with the existing communication strategy,the confidentiality in the signal modulation process is improved.The complete synchronization of the fractional-order Genesio-Tesi systems is used for signal encryption,and the validity of the designed dual-channel three-time chaotic secure communication scheme is verified by Matlab simulation.