GENERAL-METHOD OF CONTROLLING CHAOS

We present a mathematical framework for describing the allowable forms of perturbations of a control parameter for the purpose of controllin g chaos. The present paper extends the method initially proposed by Ot t, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1990)] and later ext ended by Romeiras et al. [Physica D 58, 165 (1992)], allowing for a mo re general choice of feedback forms. Among the allowable feedback form s, those that do not include the coordinates of the desired control ob ject explicitly provide a natural way to go about tracking, especially when the parameter changes are involuntary. Another benefit of the me thod is that the control can be implemented by the use of earlier stat es of the system as the feedback information. The generalized method c an be conveniently used to deal with an experimental system in the abs ence of an a priori mathematical system model where the delay coordina tes are used. These are illustrated by numerical examples in the paper .