Research On Memristor-based Chaotic Synchronization Control Method With Application

Memristor is a kind of circuit device which represents the relationship between flux and charge.It is called four basic elements of circuit together with resistance,capacitance and inductance.Because of its memory function,nonvolatile,nanostructure,high speed and nonlinearity,it has very good application value in artificial neural network,intelligent computer system,nonvolatile memory,nonlinear circuit and system and other fields.The acquisition of chaotic signal(or hyperchaotic signal)with complex dynamic characteristics and the theory of chaos synchronization control in nonlinear circuit system have always been a research hotspot.Adding a memristor to the circuit design is beneficial to the generation of more complex chaotic signals with dynamic characteristics.The emergence of memristor has opened up a new direction for the study of chaotic systems.The synchronization control of the same or different memristor chaotic system has great potential application value in the field of image encryption and secure communication.Therefore,the synchronization control and its application of the memristor chaotic system are worth studying.In this paper,taking the memristor chaotic system with unknown parameters,actuator saturation,external disturbance and internal uncertainty as the research objects,studying the sliding mode synchronization control algorithm,the finite time projection synchronization control algorithm based on the observer,the variable pulse synchronization control algorithm and the adaptive multi switch synchronization control algorithm respectively.And the adaptive multi switch synchronization control algorithm of memristor chaotic system is applied to image encryption.The main contents and innovations of this paper are summarized as follows:(1)An adaptive integral sliding mode synchronization controller is designed for the memristor hyperchaotic system with unknown parameters.Firstly,the characteristics of a hyperchaotic system with hidden attractors are analyzed,that is,the system has two positive Lyapunov exponents and no equilibrium point.Then,an adaptive integral sliding mode synchronization controller for the memristor hyperchaotic system is designed.The stability and feasibility of the synchronization control scheme are proved by using Lyapunov stability theory.Finally,the simulation results show that the memristor chaotic system can achieve synchronization quickly under the effect of adaptive integral sliding mode control strategy.(2)In view of the external disturbance and internal uncertainty of the memristor chaotic system,an observer based finite time projection synchronization control strategy is proposed.Firstly,a fourth-order memristor chaotic system is designed,and memristor and memristor chaotic circuit system are realized by analog circuit.Then,a super-twisting observer is designed to observe the external disturbances and internal uncertainties of the system.Then,a finite time controller is designed to ensure the finite time synchronization of the memristor chaotic system.Finally,the effectiveness and robustness of the proposed control strategy are verified by numerical simulation.(3)To solve the problem of actuator saturation,a variable pulse synchronization control strategy for memristor chaotic system is proposed.Firstly,a chaotic circuit model of fourth-order memristor is analyzed,and a variable pulse controller with actuator saturation is designed.Then,two kinds of pulse time window methods are used:the left end point method and the center point method.The error of the pulse input time is analyzed,and a sufficient condition to ensure the asymptotic synchronization of the memristor chaotic system is obtained.Finally,the simulation results show that the proposed variable pulse control method is more reliable than the fixed pulse control method in practical application.(4)An adaptive multi switch synchronization control strategy is designed for the high-order memristor chaotic system with uncertain parameters.Firstly,the dynamic characteristics of a high-order memristor hyperchaotic system with uncertain parameters are analyzed,and the memristor chaotic system is realized by analog circuit.Then,an adaptive multi switch controller is designed to synchronize the two hyperchaos systems.Finally,the numerical simulation results verify the effectiveness of the synchronization control strategy.(5)An adaptive multi switch synchronous image encryption algorithm for memristor chaotic system is designed.Firstly,the process of image encryption and decryption is described in detail.Then,the correlation of information before and after image encryption and the statistical analysis of histogram.Finally,the simulation results show that the designed image encryption algorithm is feasible and effective in practical application.