Stabilizing Unstable Equilibrium Points Of Chaotic Systems

Since the discovery of chaos,the problem of how to control chaos gets much attention in variousfields.In the currently available studies,there are a lot of controlling chaos methods,forexample:OGY method,delayed feedback control method and state feedback control method,etc.Atpresent,most of the methods used to control chaotic systems are on the basis of system known stateinformation.However,in practical engineering,it is difficult to obtain the entire system stateinformation or only parts of the system state information can be obtained.Therefore,in order tocontrol chaotic systems more precisely, the design of state observer and the output feedback controlmethod are used to study the problem of stabilizing unstable equilibrium point of chaotic systems inthis thesis.The main contents and contributions of the thesis are as follows:Firstly,this paper studies the problem of stabilizing unstable equilibrium point of continuouschaotic systems with unmeasured state variables using state feedback control method.First of all,design a state observer for the continuous chaotic systems;then, design state feedback controllerusing the observed state variables as the controller of the chaotic system;finally,achieve the purposeof stabilizing unstable equilibrium point of continuous chaotic systems.Secondly, we study the problem of stabilizing unstable equilibrium point of continuous chaoticsystems with unmeasured state variables using state PI regulator method.We design a state observerfor the continuous chaotic systems;then, and design a simple proportional plus integral statefeedback regulator(PI regulator)using the observed state variables as the controller of the chaoticsystem.Thirdly,the problem of stabilizing unstable equilibrium point of discrete-time chaotic systems isstudied.A state feedback controller to stabilize unstable equilibrium point of controlled discrete-timechaotic systems is designed.Considering the unmeasured state variables of controlled discrete-timechaotic systems,we design output feedback controller instead of state feedback controller.Stabilizingunstable equilibrium point of discrete-time chaotic systems is obtained finally.