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On the existence of an optimal solution of the epsilon variational problem

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Abstract

It has been shown that known sufficient conditions for existence of optimal control imply existence of an optimal solution of the nondynamic epsilon variational problem as formulated by Balakrishnan.

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References

  1. Balakrishnan, A. V.,On a New Computing Technique in Optimal Control Theory and the Maximum Principle, Proceedings of the National Academy of Sciences, Vol. 59, No. 2, 1968.

  2. Balakrishnan, A. V.,On a New Computing Technique in Optimal Control, SIAM Journal on Control, Vol. 6, No. 2, 1968.

  3. Blackwell, D.,The Range of Certain Vector Integrals, Proceedings of the American Mathematics Society, Vol. 2, No. 3, 1951.

  4. Filippov, A. F.,On Certain Questions in the Theory of Optimal Control, SIAM Journal on Control, Vol. 1, No. 1, 1962.

  5. Riesz, F., andNagy, Sz. B.,Functional Analysis, Ungar, New York, 1955.

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Additional Bibliography

  1. Balakrishnan, A. V.,On a New Computing Technique in Optimal Control and its Applications to Minimal-Time Flight Profile Optimization, Journal of Optimization Theory and Applications, Vol. 4, No. 1, 1969.

  2. Pontryagin, L. S.,et al.,The Mathematical Theory of Optimal Control Processes, John Wiley and Sons (Interscience Publishers), New York, 1962.

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  3. Neustadt, L. W.,The Existence of Optimal Control in the Absence of Convexity Conditions, Journal of Mathematical Analysis and Applications, Vol. 7, No. 3, 1963.

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Author notes

  1. A. K. Choudhury (Resident Research Associate)

    Present address: Space Systems Division, General Electric Company, Beltsville, Maryland

Authors and Affiliations

  1. Goddard Space Flight Center, Greenbelt, Maryland

    A. K. Choudhury (Resident Research Associate)

Authors
  1. A. K. Choudhury
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Communicated by A. V. Balakrishnan

This work forms a part of the doctoral dissertation submitted by the author in early 1969 at UCLA and was supported in part by the Air Force Office of Scientific Research under Grant No. 69–1646. The author expresses his gratitude to Professor A. V. Balakrishnan for many useful discussions in the preparation of this work.

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Choudhury, A.K. On the existence of an optimal solution of the epsilon variational problem. J Optim Theory Appl 11, 494–505 (1973). https://doi.org/10.1007/BF00935662

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