Analysis And Controller Design Of Fractional Order Chen Chaotic System

Fractional order chaotic system is a complex nonlinear system.Chaos has extreme sensitivity to initial values and internal randomness of phase orbits.Its existence sometimes makes the original system unable to output according to the expected results,or even makes the system collapse.At the same time,the unpredictability,concealment and more complex dynamic characteristics of chaos make it very suitable for secure communication and other research fields,and can more truly describe the actual system.Therefore,the research on the analysis and control of fractional order chaotic systems has important theoretical significance and practical research value.Based on sliding mode control,the control and synchronization of fractional-order Chen chaotic systems are studied in this paper.The main contents are as follows:Firstly,the dynamic characteristics,implementation circuit and Lyapunov exponential spectrum of fractional order Chen chaotic system are analyzed and studied.According to the fractional order stability theory,the influence of the order of fractional order Chen system on the stability of the system is studied.Through theoretical deduction,if the differential order?>0.83 of the system,the fractional order Chen system is chaotic at this time.Then,the correctness of the theoretical derivation is verified by the numerical simulation images of fractional order Chen system,circuit simulation images and Lyapunov exponential spectra of fractional order Chen system of different orders.Secondly,the control of fractional Chen chaotic system is studied.Firstly,a non-linear controller is designed to control fractional-order Chen chaotic system with and without disturbance.The simulation results show that the designed non-linear controller does not have good anti-jamming ability.Then,based on the sliding mode control theory,a fractional sliding mode controller is designed to control the fractional Chen chaotic system with known disturbance upper bound.The simulation results show that the designed fractional-order sliding mode controller can make the controlled fractional-order Chen chaotic system asymptotically stable,and has good robustness to external disturbances,but its rapidity is poor.Therefore,this paper improves the sliding mode controller and designs an adaptive sliding mode controller,which effectively improves the corresponding rapidity of the system.Finally,the synchronization control of fractional Chen chaotic system is studied.A fractional-order sliding mode synchronization controller is designed to synchronize the fractional-order Lorenz chaotic system and the fractional-order Chen chaotic system with unknown disturbance upper bound,using the fractional-order Lorenz chaotic system as the driving system and the fractional-order Chen chaotic system as the response system.The simulation results show that the designed sliding mode synchronization controller has robustness and can achieve complete synchronization between the two systems,but its rapidity is poor.In this paper,the sliding mode synchronization controller is improved with adaptive control,which further improves the rapidity and stability of the error system.Finally,by combining the improved sliding mode controller with the generalized synchronization,the fast generalized synchronization of the four-dimensional fractional-order hyperLorenz chaotic system and the three-dimensional fractional-order Chen chaotic system is realized,which makes the chaotic synchronization more secure and fast in secure communication.