Non-periodic Orbits Of Chaotic Systems, Control Methods And Applications

Chaotic control is a new theory ,which is first developed by E.Ott,G.Grebogi and J.Yorke at the end of last century. The main innovations embodied in this field are the present of the concept of chaos and strange attractor. Chaotic system is a natural phenomenon in actual world. The essential aim of chaotism is to describe this phenomenon and uncover its law so that people can take advantage of those kinds of chaotic systems. Generally, chaotic control means to control a chaotic system to be a system with expected features and performances.The conception of chaos was regarded as a physical problem before, however it has been applied in some actual engineering problems. The chaotic control has important theoretical value and widely applying perspective.At the beginning, this paper introduces the development of chaos. Next it discusses some classical method of chaotic control. At the same time some examples are presented. Based on the research and conclusion of the former works and achievements, this paper gives us a new idea, 'non-periodic orbit control of chaotic system'. All the control methods before aimed to let chaotic systems stable, however, this article chooses a non-periodic signal as the target order and controls Lorenz system through continuous feedback control method. This paper describes the basic principle and makes out the numerical results. The method's main significance is to put forward a novel form , which is called 'non-linear controls non-linear'. Based on this method, a new Chaos-based security communication idea comes up.The transformation of signals can be bi-controlled, that is mutual calling. Finally, this paper concludes that the utilization of non-linear and non-stationary character of systems is better than the ignorance of it, so we should extract more fault characteristics and try to obtain more good ones.