Synchronization Of A Class Of Time-delay Chaotic System

There are lots of chaotic phenomena in the real world, such as Lorenz systems in the meteorology, Chua's circuit system and so on. Because chaotic system is extremely sensitive to the initial condition which make the system output not meet people's demand, we always need to restrain the chaos in many practical systems. On the other hand, the chaotic system can be beneficial to other systems due to its hard prediction and inner random, Such as, the application of chaos to the secure communications. So it is very important to chaos control and application about how to restrain chaos when it is harmful and how to make use of it when it is useful. And the research on it will have theoretical and real applied value.In this thesis, we draw some results of chaos synchronization through the study of chaos systems, methods of control and synchronization. First, nonlinear system is discussed, some research methods about it are introduced. Second, some basic notions and definitions about chaos study are systematically introduced, then the main characters of chaos, the way to chaos and the methods of control chaos, the definition of chaos synchronization, the category and the methods of it are introduced too. Furthermore, some algorithms of system identification about chaos system are introduced. By the discussion of persistency of excitation, a shortcoming of the algorithm of an adaptive synchronization is pointed out. And then, the problem on a class of time-delay chaos synchronization is discussed, when the parameter is unknown, by the design of controller, the synchronization of this time-delay chaos system is realized, then a parameter estimation converges to the real value. Based on the theory of Lyapunov's, synchronization controller is constructed, through the theory of persistency of excitation in model reference adaptive control, the condition that the parameter converges to the real value is given. Finally, the conclusions of the whole thesis are given.