| The chaos phenomenon is one of the most important science discoveries. In the last two decades, researches of chaos was mainly concentrated in quantification from experiments and numerical simulations. Along with the further understanding of chaos phenomenon, how to apply the chaos research archivement to serve for the humanity has became one important topic which the non-linear science developments proposed. It's main reason is: on the one hand, the application of chaos will directly drive the new research enthusiathm; on the other hand, the application of chaos proposes new questions will be able to promote the further chaos research effectively. As a significant result, people certainly concerned whether we can apply these result into applicatoin. Because the chaos is characterized by"supersensitivity"to the initial conditions and long term forcasts of trajectories are impossible, control of chaos becomes the essential link to application. Therefore, researchers began to study how to control and utilize chaos phenomenon.This paper introduced the general concept of chaos with several common definitions. To make the introduction illustrative, some examples with figures were given. Some properties of dynamcal system related to control were given. In the third charpter, some methods to control chaos and synchronization chaos were reviewed. In the fourth chapter, an important control theory, implusive control theory, was discussed in detail, including some elementary knowledge about impulsive differential equations. Again regarding different impulsive control system: the linear impulsive control systems and the non-linear implusive control systems were introduced and corresponding achivements were discussed in detail.. Although these achievements have already been developed for a long time. But until now, it is still not wide-spread. Therefore, to a certain extent, we elaborated these theories which would serve as the preparation for the introduction of my reseach results. These results included: the complete synchroniztion of most of chaos systems. I took th Lorenz and unified chaotic systems as demostrations Apart from these, Chuangdong Li's method of converting a synchronization problem into an optimization problem were also introduced. By this method, a proper value of control parameter can be obtained. |
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