The Study On The Control Of The Chaotic Nonlinear Dynamical Systems And The Chaotic Secure Communication Systems

This dissertation investigates some control methods of the control chaotic nonlinear dynamical systems and the chaotic secure communication systems. Variable feedback control method, the control method based on the symbolic dynamics, signal exaction of chaotic secure communication systems in terms of the reconstruction, the design of digital chaotic secure communication are researched.In chapter 1, the signification of the research and the recent research results in the world are introduced briefly.The researches in chapter 2 are all based on the variable feedback control method. Firstly, we use norm theory to research the controlled chaotic systems and lead to some sufficient conditions for system convergence and the choice of state feedback gain matrixes. Secondly, we investigate the controlled chaotic system in the situation where system parameter error or noise exist and deduce the relationship between the parameter error or noise with the deviation of the stable orbit. Finally, when the approximate unstable periodic orbits (UPO) are used in the control and the controlled systems are stable, we deduce the relationship between the difference of the stable orbit and the approximate UPO and the difference of the stable orbit and the real UPO. A method to correct the stable orbit onto the real UPO is developed in tenns of this relationship.In chapter 3, we propose a new method to control chaotic systems. Firstly we use the symbolic dynamics to coarse-grainedly divide the chaotic attractor. Then, based on the properties of chaotic system which is sensitive to noise and can be predicted in the short time interval, we use small control quantity to predictive control the chaotic system to make it evolve along the orbits which are represented by the set symbolic sequence.In chapter 4, we proposed a message exaction method which basing on the system reconstruction and one-step predictions to exact the message from simulative chaotic secure communication systems. After the system reconstruction and one-step prediction, we deduce the relationship between the difference of the transmitted signal and the predicted signal and the message. Using this relationship, we can extract the message directly.In chapter 5, we design a new digital chaotic secure communication system that is based on the chaotic synchronization. The system uses the one dimension nonlinear functions to represent the digital message and uses the proper linear part to realize the system synchronization.