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An existence theorem for a fractional control problem

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Abstract

Computational algorithms in mathematical programming have been much in use in the theory of optimal control (see, for example Refs. 1–2). In the present work, we use the algorithm devised by Dinkelback (Ref. 3) for a nonlinear fractional programming problem to prove an existence theorem for a control problem with the cost functional having a fractional form which subsumes the control problem considered by Lee and Marcus (Ref. 4) as a particular case.

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References

  1. Van Slyke, R. M.,Mathematical Programming and Optimal Control, University of California at Berkeley, Ph.D. Thesis, 1965.

  2. Goldstein, A. A.,Convex Programming and Optimal Control, SIAM Journal on Control, Vol. 3, No. 1, 1965.

  3. Dinkelback, W.,On Nonlinear Fractional Programming, Management Science, Vol. 13, No. 7, 1967.

  4. Lee, E. B., andMarkus, L.,Optimal Control for Nonlinear Processes, Archive for Rational Mechanics and Analysis, Vol. 8, No. 1, 1961.

  5. Coddington, E. A., andLevinson, N. L.,Theory of Ordinary Differential Equations, McGraw Hill Book Company, New York, 1955.

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  6. Courant, R.,Differential and Integral Calculus, Vol. 2, John Wiley and Sons (Interscience Publishers), New York, 1962.

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Author notes

  1. S. K. Bhatt

    Present address: the Indian Statistical Institute, Calcutta, India

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Kanpur, India

    S. K. Bhatt

Authors
  1. S. K. Bhatt
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Additional information

Communicated by G. B. Dantzig

The author is thankful to the referee for suggestions.

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Bhatt, S.K. An existence theorem for a fractional control problem. J Optim Theory Appl 11, 379–385 (1973). https://doi.org/10.1007/BF00932487

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  • DOI: https://doi.org/10.1007/BF00932487

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