A new method of adaptive tracking control for chaotic system

Abstract

In this paper, a new strategy of adaptive tracking control of chaotic system is proposed.By designing the compensatory controller in advance, this method transforms the tracking control problem of reference signals which are tracked by chaotic system states variables into the adaptive synchronization problem of identical-structured chaotic system variables. Tracking controller is equal to the sum of compensatory controller and adaptive controller.Truth of tracking controller designed by proposed strategy is proved theorically based on Lyapunov stability theory.Finally, taking hyperchaotic Chen system as controlled object, tracking controllers are designed in this way to track fixed points, sine signals, cosine signals, identical-structured chaotic system state variables and different-structured chaotic system state variables. The response time is very short, showing the effectiveness of the strategy.