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Hereditary optimal control problems: Numerical method based upon a padé approximation

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Abstract

In this paper, we consider a particular approximation scheme which can be used to solve hereditary optimal control problems. These problems are characterized by variables with a time-delayed argumentx(t − τ). In our approximation scheme, we first replace the variable with an augmented statey(t) ≜x(t - τ). The two-sided Laplace transform ofy(t) is a product of the Laplace transform ofx(t) and an exponential factor. This factor is approximated by a first-order Padé approximation, and a differential relation fory(t) can be found. The transformed problem, without any time-delayed argument, can then be solved using a gradient algorithm in the usual way. Four problems are solved to illustrate the validity and usefulness of this technique.

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Author notes

  1. A. Y. Lee (Graduate Student)

    Present address: General Motors Research Laboratories, Warren, Michigan

Authors and Affiliations

  1. Stanford University, Palo Alto, California

    A. Y. Lee (Graduate Student)

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  1. A. Y. Lee
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Additional information

Communicated by G. Leitmann

This research was supported in part by the National Aeronautics and Space Administration under NASA Grant NCC-2-106.

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Lee, A.Y. Hereditary optimal control problems: Numerical method based upon a padé approximation. J Optim Theory Appl 56, 157–166 (1988). https://doi.org/10.1007/BF00938531

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  • DOI: https://doi.org/10.1007/BF00938531

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