Control And Synchronization For The New Multi-scroll Chaotic System

Comparing with traditional chaotic systems,multi-scroll chaotic systems have more complex dynamic characteristics and more key parameters.Multi-scroll chaotic systemsare more widely used in chaotic system information encryption.At present,the research of multi-scroll chaotic systems is mainly focused on constructing the appropriate nonlinear function to produce multi-scroll chaotic systems,but the analysis of multi-scroll chaotic systems is not very sufficient.It is difficult to analyze by traditional dynamic theory.And the traditional control theory is difficult to study the multi-scroll chaotic systems.Most researches on multi-scroll chaotic systems athome and abroad are less.But the control and synchronization of multi-scroll chaotic systems still have high application value and development prospect for engineering application.In this paper,the multi-scroll chaotic system is generated on the basis of Jerksystem.Unidirectional scrolls and complexity are increased.The divergence,equilibrium point,Lyapunov exponent,Lyapunov dimension,bifurcation and other basic dynamics of the new multi-scroll chaotic system are analyzed.The chaotic characteristics of the system are verified by numerical simulation and the circuit experiments.The new multi-scroll chaotic system is tracked by the nonlinear feedback control method,the sliding mode variable structure control method and the linear feedback sliding mode control method.Compared with the nonlinear feedback method and the sliding mode variable structure control method,the tracking target time is shortened by the linear feedback sliding mode control method,and the tracking effect is improved.The effectiveness of the three methods has been demonstrated by numerical simulation and circuit experiments.Finally,the synchronization of the new multi-scroll chaotic system is studied by active control method,active sliding mode control method,adaptive sliding mode control method,linear feedback method and linear feedback sliding mode control method.Compared with the active control method,the time of the synchronization for the drive system and response system is shortened by active sliding mode control method.But the controller of the active sliding mode control methodis more complex.Compared with the active sliding mode control method,the two systems can also reach the synchronization through the adaptive sliding mode control,and the complexity of the controller is simplified.Linear feedback controller is simple,physical experiments are easy to achieve,but synchronization time is long,robustness is weak.Linear feedback sliding mode control theory is proposed by combining linear feedback control theory with sliding mode variable structure control theory.Compared with the active sliding mode control method and the adaptive sliding mode control method,the two systems reach the synchronization time is shortened by the linear feedback sliding mode.And synchronization effect is improved.Compared with the linear feedback method,the linear feedback sliding mode control method has strong anti-interference ability and strong robustness.