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An elementary proof of the maximum principle for optimal control problems governed by a Volterra integral equation

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Abstract

An elementary proof of the maximum principle for optimal control problems whose states are governed by Volterra integral equations is given. Our proof is motivated by the work of Michel (Ref. 7) and utilizes only elementary results from analysis and mathematical programming. By appealing to Pontryagin-type perturbations of the controls, the above optimal control problem is effectively reduced to a mathematical programming problem. The results are then obtained by appealing to well-known mathematical programming results.

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Authors and Affiliations

  1. Department of Mathematics, Southern Illinois University at Carbondale, Carbondale, Illinois

    D. A. Carlson (Assistant Professor)

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  1. D. A. Carlson
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Communicated by L. Cesari

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Carlson, D.A. An elementary proof of the maximum principle for optimal control problems governed by a Volterra integral equation. J Optim Theory Appl 54, 43–61 (1987). https://doi.org/10.1007/BF00940404

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