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Dinkelbach Approach to Solving a Class of Fractional Optimal Control Problems

Author

Listed:
  • I. Bykadorov

    (Sobolev Institute of Mathematics, Siberian Branch Russian Academy of Sciences)

  • A. Ellero

    (Università Ca’ Foscari)

  • S. Funari

    (Università Ca’ Foscari)

  • E. Moretti

    (Università Ca’ Foscari)

Abstract

We consider optimal control problems with functional given by the ratio of two integrals (fractional optimal control problems). In particular, we focus on a special case with affine integrands and linear dynamics with respect to state and control. Since the standard optimal control theory cannot be used directly to solve a problem of this kind, we apply Dinkelbach’s approach to linearize it. Indeed, the fractional optimal control problem can be transformed into an equivalent monoparametric family {Pq} of linear optimal control problems. The special structure of the class of problems considered allows solving the fractional problem either explicitly or requiring straightforward classical numerical techniques to solve a single equation. An application to advertising efficiency maximization is presented.

Suggested Citation

  • I. Bykadorov & A. Ellero & S. Funari & E. Moretti, 2009. "Dinkelbach Approach to Solving a Class of Fractional Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 55-66, July.
    • Handle: RePEc:spr:joptap:v:142:y:2009:i:1:d:10.1007_s10957-009-9540-5
    DOI: 10.1007/s10957-009-9540-5
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    References listed on IDEAS

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    1. Gustav Feichtinger & Richard F. Hartl & Suresh P. Sethi, 1994. "Dynamic Optimal Control Models in Advertising: Recent Developments," Management Science, INFORMS, vol. 40(2), pages 195-226, February.
    2. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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