CONTROLLING CHAOS USING NONLINEAR APPROXIMATIONS AND DELAY COORDINATEEMBEDDING

In a previous paper we showed that a chaos control method proposed by Ott, Grebogi and Yorke can be improved by using nonlinear approximatio ns for chaotic dynamical systems and stable manifolds of targets. Here we consider systems whose governing equations are unknown and apply t he chaos control method using the nonlinear approximations. Delay coor dinate embedding techniques are used, so that approximate saddle point s to be stabilized and nonlinear approximations of the systems and sta ble manifolds are obtained from time series of single variables. We al so take into account the fact that the obtained section maps depend on the current and previous parameters. To demonstrate our approach, we give two numerical examples for the Henon map and a pendulum with feed forward and feedback control. Some influences of noise are also discus sed in these examples. (C) 1998 Elsevier Science B.V.