Abstract
In this paper we derive necessary conditions, in the form of a maximum principle, for the optimal control of nonlinear, finitely retarded functional differential equations with function-space boundary conditions. We establish these conditions in a setting which guarantees the existence of regular multipliers, admits pointwise control constraints, and, with added restrictions, ensures nontriviality of the multipliers.
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The referee has kindly pointed out the following relevant references which merit inclusion here
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The majority of this work was done while the first author was guest at the Institute für Numerische und Angewandte Mathematik der Universität Göttingen, Göttingen, BRD.
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Angell, T.S., Kirsch, A. On the necessary conditions for optimal control of retarded systems. Appl Math Optim 22, 117–145 (1990). https://doi.org/10.1007/BF01447323
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DOI: https://doi.org/10.1007/BF01447323