利用Lyapunov指数的混沌控制及控制参数选择

自1990年,美国马里兰大学的Ott,Grebogi和Yorke三人首先从理论上提出控制混沌的方法,即OGY方法,混沌控制已成了非线性理论及应用中重要的组成部分但混沌控制(OGY)方法在数学理论上还有许多工作需要完善,从数学理论上对OGY方法进一步论证和探讨,对混沌控制理论的建立和体系化有很重要的意义而笔者利用Lyapunov指数讨论了混沌控制(OGY方法)有效的充分条件,获得了具体的表示式并将此方法用于讨论具体的控制参数的选择及控制参数所须满足的条件最后对二维Henon映射的轨道稳定化控制的有效性给出了解释

Controlling Chaos Using Lyapunov Exponents and Study of Controlling Parameters

In 1990, Ott, Grebogi and Yorke from university of Maryland in U.S.A proposed a new way to achieve controlling of chaos OGY method. Since then,controlling chaos has become an important part of nonlinear theory and application. But as a mathematics theory there is still a lot to be perfected in controlling chaos(OGY method).The further proof and discussion of OGY method in mathematics theory are of great significance for building up the controlling chaos theory and system.Using Lyapunov exponents for the moment the authors obtain the expression by discussing the effectively sufficient condition of controlling chaos (OGY method).Then the above method is applied to discuss the selection of control parameters and the condition the control parameters must satisfy. Finally, we give an explanation of effeciency of 2D Henon map's orbit stablization controlling.