Analysis And Control Of Several Discrete Chaotic Systems

Chaos and control in the field of nonlinear systems has gradually become a hot research topic.Chaos in nature has attracted the attention of scholars.Chaos involves many fields,including medicine,biology,economy,information,control and so on.In the research of practical problems,the continuous system can be transformed into discrete system according to Poincare section method.Therefore,the research on chaos and control of discrete system is of universal significance.Since OGY method was proposed,many discrete chaos control methods have been proposed successively,including feedback control method and non feedback control method.In this paper,two-dimensional Ushiki discrete system,two-dimensional cubic discrete system,BVP oscillator discrete system and abnormal three-dimensional discrete system are studied.Lyapunov exponent allocation method,chaotic trajectory tracking control and backstepping method are applied.The specific research contents are as follows:(1)The chaos control problem of two-dimensional Ushiki discrete system is studied.Firstly,by drawing the Lyapunov exponent spectrum and waveform of the system,the stability of the fixed point is analyzed,and the existence of chaotic attractor is confirmed.Secondly,by analyzing the complex dynamic bifurcation diagram of the discrete system,the characteristics of Ushiki discrete system are expressed by changing parameter.Then,two different controllers are designed by using Lyapunov exponent collocation method and nonlinear feedback linearization chaotic trajectory tracking control method,and the effectiveness of the controller is verified by numerical simulation.(2)The chaos control problem of two-dimensional cubic discrete system is studied.Firstly,by drawing the Lyapunov exponent spectrum and waveform of the system,the stability of the fixed point is analyzed,and the existence of chaotic attractor is confirmed.Secondly,the complex dynamics bifurcation diagram of discrete system is analyzed.Then,two different controllers are designed by using nonlinear feedback linearized chaotic trajectory tracking control method and backstepping method,and the effectiveness of the controller is verified by numerical simulation.(3)The chaos control problem of BVP oscillator discrete system is studied.Firstly,by drawing the Lyapunov exponent spectrum and waveform of the system,the stability of the fixed point is analyzed,and the existence of chaotic attractor is confirmed.Then,two different controllers are designed by using nonlinear feedback linearized chaotic trajectory tracking control method and backstepping method,and the effectiveness of the controller is verified by numerical simulation.(4)The chaos control of abnormal three-dimensional discrete systems is studied.Firstly,by drawing the Lyapunov exponent spectrum and waveform of the system,the stability of the fixed point is analyzed,and the existence of chaotic attractor is confirmed.Then,two different controllers are designed by using Lyapunov exponent collocation method and nonlinear feedback linearization chaotic trajectory tracking control method,and the effectiveness of the controller is verified by numerical simulation.