Chaos control for a class of nonlinear system

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, Rössler 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 atlractors 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.