Optimal control of chaos with synchronization

Optimal control of chaotic systems is discussed in this paper. Since often only open-loop control can be obtained from the minimum principle, the output of the controlled system may be dramatically affected by noise. By using chaos synchronization, we successfully keep the output of the controlled chaotic system in the designed optimal trajectory even in noisy background. The numerical experiments of the Rossler system and the Henon system are presented to demonstrate its effectiveness.