| Chaos,as an important part of the nonlinear field,it has attracted the attention of a large number of scholars because of its wide application in the fields of electronics,meteorology,secure communications and image encryption.With the rapid development of technologies such as semiconductors,the research on synchronization control based on chaotic systems has been widely developed in various fields,especially in the fields of secure communications and image encryption,which have potential practical value.Because high-order chaotic systems have stronger unpredictability and more complex nonlinear characteristics than low-order chaotic systems,the synchronization control of high-order chaotic systems has received widespread attention.At present,there are many studies on the same-order chaotic synchronization control,but relatively few studies on the different-order chaotic synchronization control.At the same time,considering the practicability of synchronization control of different-order chaotic systems,the influence of uncertainty factors and convergence rate on chaotic synchronization control must be fully considered,and the finite-time synchronization control of uncertain different-order chaotic systems must be thoroughly studied.In addition,how to extend the synchronization control of the ordinary double chaotic systems to the synchronization control of the multi-chaotic systems,so that it can provide a reliable guarantee for the security encryption technology based on the synchronization of the multi-chaotic systems,is also worthy of further research.Especially in recent years,chaotic system based on memristor has become a hot research topic in the field of nonlinear control systems due to its stronger pseudo-randomness and more complex chaotic signals.Therefore,it is of great theoretical significance and potential practical value to study the synchronization control of different-order chaotic systems,the synchronization control of multi-chaotic systems,the synchronization control of chaotic systems based on memristor and the synchronization control circuits of chaotic systems and their applications.Through learning and research,the main research results have been achieved:(1)For the chaotic synchronization control of the different-order Rabinovich systems,a reduced-order synchronization control and an increased-order synchronization control of the different-order Rabinovich systems are realized by passive control and sliding mode control theory respectively.At the same time,the global asymptotic stability of the chaotic synchronization error system is proved by Lyapunov stability theory and the Routh-Hurwitz stability criterion.Through numerical simulation,the advantages and disadvantages of the two control methods are compared and analyzed,and the effectiveness of the designed controller is shown.(2)For the synchronization control of uncertain different-order chaotic systems with unknown parameters,two chaotic synchronization controllers are proposed,including adaptive controller and terminal sliding mode controller.Based on the adaptive law method,the unknown parameters,model uncertainties and external interference terms in the system model are estimated.Through the finite-time stability theorem,combined with the adaptive control strategy,the finite-time adaptive control method and the terminal sliding mode control method are used to overcome the influence of the nonlinear input of the controller on the synchronization of the different-order chaotic systems,and the reduced-order and increased-order synchronization control of the different-order chaotic systems are realized,respectively.(3)For the projective synchronization control of uncertain multi-chaotic systems,two chaotic synchronization modes are discussed,including one-to-many chaotic synchronization and transfer chaotic synchronization,and a finite-time chaotic synchronization controller based on super-twisting observer is designed respectively.Based on the theory of finite time stability,using the quadratic Lyapunov function,the sufficient conditions for the synchronization of the observer error system are derived,and the uncertainty of the system is estimated.On this basis,a finite-time controller is proposed,which simplifies the chaotic synchronization system model and achieves finite-time convergence of the chaotic synchronization error system.In addition,based on transfer chaotic synchronization,the feasibility of chaotic masking encryption communication scheme is explored,which provides more options for secure communication based on chaotic synchronization.(4)A chaotic synchronization control of memristor based on a single feedback controller is studied.By describing a memristor-based chaotic system model,a single feedback chaotic synchronization controller is proposed,which is beneficial to the realization of subsequent chaotic synchronization control circuits.At the same time,based on the Routh-Hurwitz stability criterion and the minimum phase theory,a sufficient condition for chaotic synchronization control based on a single feedback controller is obtained.In addition,the use of DNA coding technology to further encode the color image encrypted based on the chaotic sequence improves the image security during the encrypted transmission process,and shows the effectiveness of the image secure communication based on the chaotic synchronization of the memristor.(5)The design and implementation of a chaotic synchronization control circuit based on memristor is studied.A chaotic circuit model based on an active magnetic memristor is designed and implemented After the actual hardware circuit test,the result verifies the double vortex attractor structure of the memristor chaotic circuit.On this basis,a single feedback chaotic control circuit is designed and implemented,and the synchronization control of the memristor chaos is realized from the circuit.The test results show that the single feedback chaos control can effectively achieve the synchronization control of the memristor chaos,and the controller is simple and effective.In addition,on the basis of the memristor chaotic synchronization control circuit,a signal secure communication experiment is carried out.The experimental results show that the single feedback chaotic control synchronization secure communication scheme is feasible. |
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