一类非线性系统的混沌控制

Chaos Control for a Class of Nonlinear System

描述航天器、陀螺和气浮台等刚体姿态运动的欧拉动力学方程,是一个具有广泛代表意义的三阶非线性方程。当该方程中的参数取不同值时,可得到著名的Lorenz系统、Rssler系统、Newton-Leipnik系统、Chen系统及L系统诓煌耐饬刈饔孟?该动力学系统会呈现出相当复杂的动力学行为。从该系统中,发现了一大类新的混沌吸引子。本文分析了这一类混沌吸引子具有的共同特征,并采用基于输出反馈的PI型控制器将一种新的混沌运动稳定于指定平衡点。仿真结果表明,该控制器能够有效地抑制混沌,能将系统稳定于任意指定的不稳定平衡点。

The Euler’s dynamical equation which describes the attitude motion of a rigid body （such as spacecraft, gyroscope, 3-axis air bearing table etc.） is a more generalized 3-dimensional nonlinear system. Some well-known chaotic systems （such as Lorenz system, Rssler system, Leipnik-Newton system, Chen system, Lü system etc.） can be educed from this equation by altering the parameter values. This dynamical system will exhibit very complex dynamic behaviors under the influence of different external torques. A series of new chaotic attractors are found from this system. In this paper, the common characteristics of these chaotic attractors are analyzed and a controller based on the PI-type output feed back is developed to stabilize a new chaotic motion to an appointed equilibrium point. The simulation result indicates that this control method can suppress the chaos and can regulate the state trajectory of this system to the given fixed point.