The Application Of Impulsive Control Theory In Chaotic System

Chaos is one of the most important discoveries in the 20th century. In the last two decades, researches on chaos mainly cover the observation from experiments and the quantification from numerical simulations. Along with the further understanding of chaos, one important issue occurs, i.e., how to apply the research achievements to serve for the humanity. The main reasons are: on the one hand, the application of chaos will directly inspire the new research enthusiasm; on the other hand, the application of chaos will lead to new questions which will be able to promote the chaos research effectively. Because chaos is characterized by"supersensitivity"to the initial conditions and long term non-forecasts of trajectories, control of chaos is of much importance for the application. Therefore, many researchers have been studying how to control and utilize chaotic sytems.This paper restates the general concept of chaos in terms of several common definitions. To make the introduction illustrative, some examples with figures are given. Several dynamical properties of chaotic systems, which are related to control, are also presented. In the third charpter, some methods for controlling and/or synchronizing chaos are outlined. In the fourth chapter, impulsive linear and nonlinear control theory, together with some elementary knowledge about impulsive differential equations, is discussed in detail. Meanwhile, the corresponding achievements are also given. Although these results have already been derived for a long time, they have been playing a positive role until now, namely, they are the foundation of the further reseach results in the current study. In this endeavour, the design of the chaos controller is proposed. As examles, Rossler system and unified chaotic system are presented to demonstrate the validity of the proposed method, and an estimated upper bound of the impulsive period is also given. Finally, based on the LMI technique, the synchronization problem is transformed into the optimization problem, which allow us to derive a proper value of control parameter.