Control Research Of Several Chaotic Memory Oscillation Systems

Since American meteorologist Lorenz discovered the world’s first chaotic model in 1963,the related research of chaotic system began to develop gradually and became a hot academic research.Many chaotic phenomena in nature that people pay attention to can be applied to medicine,mechanics,biology,information,economy and other fields after being studied.In the study of chaotic system,the dynamic behavior of chaotic system can be analyzed by drawing Lyapunov exponential diagram and bifurcation diagram.In order to stabilize the chaotic system to the equilibrium point,many control methods are born.In this paper,three-dimensional Coullet system,solar wind driven magnetosphere-ionosphere system and double vortex system(all of which belong to chaotic memory oscillation system)are taken as the research objects,and a variety of control methods are applied to control the chaotic state of chaotic memory oscillation system.Specific research contents are as follows:(1)For the three-dimensional Coullet system,the chaos state and control problem are studied.Firstly,the existence of chaos is verified by drawing the time domain waveform diagram,chaotic attractor diagram,bifurcation diagram and Lyapunov exponent diagram of the system.Then,a variety of different controllers are designed using feedback linearization control,adaptive control,sliding mode based high-frequency robust control and high gain robust control.Finally,the effectiveness of the controllers is verified by numerical simulation.(2)The chaotic state and control of magnetosphere-ionosphere system driven by solar wind are studied.Firstly,the existence of chaos is verified by drawing the time domain waveform diagram,chaotic attractor diagram,bifurcation diagram and Lyapunov exponent diagram of the system.Then,using the sliding mode based high-frequency robust and high-gain robust control and Backstepping control methods,a variety of different controllers are designed.Finally,the effectiveness of the controllers is verified by numerical simulation.(3)The chaos state and control of the two-vortex system are studied.Firstly,the existence of chaos is verified by drawing the time domain waveform diagram,chaotic attractor diagram,bifurcation diagram and Lyapunov exponent diagram of the system.Then,using the sliding mode based high-frequency robust and high-gain robust control and Backstepping control methods,a variety of different controllers are designed.Finally,the effectiveness of the controllers is verified by numerical simulation.Finally,according to the control effect of various chaos control methods,the different kinds of methods are compared,and the advantages of their characteristics and improvement methods are expounded.