Research On Control Methods Based On A Class Of Chaotic Systems

The development of nonlinear dynamics is one of the most significant achievements in the field of natural sciences in the late 20 th century,especially the discovery of chaotic motion,which breaks the deep-rooted determinism in the field of physics and makes researchers begin to re-examine the world.Chaotic motion is ubiquitous in our actual production and life.It refers to a form of motion that obeys the law of certainty but has randomness,which reveals the relevance,complexity and unpredictability of all activities in the nature under a long time span.The study of chaos phenomenon is conducive to our better understanding and transformation of the world.Therefore,chaos control has increasingly become the focus of nonlinear dynamics researchers.Various control methods emerge one after another and have been applied in plenty of fields in combination with practice.In this context,based on the theory of chaos and the definitions and theorems in the stability theory of nonlinear systems,this paper focuses on the tracking control and finite time tracking control of several integer and fractional chaotic systems.The major work of this paper is as follows: firstly,some preliminary knowledge including chaos theory,chaos control theory,stability theorem of nonlinear system,definition and properties of fractional calculus are introduced.Secondly,the tracking control of integer order chaotic system and fractional order chaotic system is studied and verified by numerical simulation.Furthermore,on the basis of tracking control,the finite time stability theorem is introduced,the tracking control and finite time control are combined,the finite time tracking control theory is proposed,which is respectively applied to integer order hyper-chaotic system and fractional order chaotic system,and verified by numerical simulation.Finally,the full paper is summarized and prospected.