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On the optimality of the Ott-Grebogi-Yorke control scheme

Publication ,  Journal Article
Epureanu, BI; Dowell, EH
Published in: Physica D: Nonlinear Phenomena
January 1, 1998

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.

Duke Scholars

Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

January 1, 1998

Volume

116

Issue

1-2

Start / End Page

1 / 7

Related Subject Headings

  • Fluids & Plasmas
  • 4903 Numerical and computational mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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Epureanu, B. I., & Dowell, E. H. (1998). On the optimality of the Ott-Grebogi-Yorke control scheme. Physica D: Nonlinear Phenomena, 116(1–2), 1–7. https://doi.org/10.1016/S0167-2789(97)00252-2
Epureanu, B. I., and E. H. Dowell. “On the optimality of the Ott-Grebogi-Yorke control scheme.” Physica D: Nonlinear Phenomena 116, no. 1–2 (January 1, 1998): 1–7. https://doi.org/10.1016/S0167-2789(97)00252-2.
Epureanu BI, Dowell EH. On the optimality of the Ott-Grebogi-Yorke control scheme. Physica D: Nonlinear Phenomena. 1998 Jan 1;116(1–2):1–7.
Epureanu, B. I., and E. H. Dowell. “On the optimality of the Ott-Grebogi-Yorke control scheme.” Physica D: Nonlinear Phenomena, vol. 116, no. 1–2, Jan. 1998, pp. 1–7. Scopus, doi:10.1016/S0167-2789(97)00252-2.
Epureanu BI, Dowell EH. On the optimality of the Ott-Grebogi-Yorke control scheme. Physica D: Nonlinear Phenomena. 1998 Jan 1;116(1–2):1–7.
Journal cover image

Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

January 1, 1998

Volume

116

Issue

1-2

Start / End Page

1 / 7

Related Subject Headings

  • Fluids & Plasmas
  • 4903 Numerical and computational mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics