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On the Existence of Optimal Solutions to an Optimal Control Problem

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Abstract

In this paper, some results concerning the existence of optimal solutions to an optimal control problem are derived. The problem involves a quasilinear hyperbolic differential equation with boundary condition and a nonlinear integral functional of action. The assumption of convexity, under which the main theorem is proved, is not connected directly with the convexity of the functional of action. In the proof, the implicit function theorem for multimappings is used.

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Authors and Affiliations

  1. Department of Mathematics, University of Lodz, Lodz, Poland

    M. Majewski (Assistant Professor)

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  1. M. Majewski
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Communicated by L. D. Berkovitz

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Majewski, M. On the Existence of Optimal Solutions to an Optimal Control Problem. J Optim Theory Appl 128, 635–651 (2006). https://doi.org/10.1007/s10957-006-9036-5

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  • DOI: https://doi.org/10.1007/s10957-006-9036-5

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