CONTROLLING CHAOTIC DYNAMIC-SYSTEMS

We describe a method that converts the motion on a chaotic attractor to a desired attracting time periodic motion by making only small time dependent perturbations of a control parameter. The time periodic motion results from the stabilization of one of the infinite number of previously unstable periodic orbits embedded in the attractor. The present paper extends that of Ott, Grebogi and Yorke [Phys. Rev. Lett. 64 (1990) 11%], allowing for a more general choice of the feedback matrix and implementation to higher-dimensional systems. The method is illustrated by an application to the control of a periodically impulsively kicked dissipative mechanical system with two degrees of freedom resulting in a four-dimensional map (the "double rotor map"). A key issue addressed is that of the dependence of the average time to achieve control on the size of the perturbations and on the choice of the feedback matrix.