On the optimality of the Ott-Grebogi-Yorke control scheme
Some of the characteristics of the Ott-Grebogi-Yorke (OGY) control technique are presented as applied to nonlinear flows, as distinct from nonlinear maps. Specifically, we consider the case where the magnitude of the control parameter varies in time within each control cycle in proportion to a given function referred to as a basis function. The choice of the basis function is shown to influence the basin of convergence for a given level of parameter variation in the OGY controller. An algorithm for designing the optimal basis function is presented. The optimal basis function is shown to be defined by a step function with potentially several jumps, thus revealing the intrinsic power of a standard OGY technique that uses a single step function as a basis function. Two numerical applications of the optimal design technique to a Duffing oscillator are also presented to show that the standard OGY technique may be significantly improved by making an optimal choice of a basis function. Copyright © 1998 Elsevier Science B.V.
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