Geodesic
Volterra functional equations and optimization of distributed systems. Special optimal controls
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 2, Tome 209 (2022), pp. 53-76

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The work is a brief review of some results of optimization theory obtained by using Volterra functional equations (VFE). We present the method proposed by the author for using the VFE-description of controlled initial-boundary-value problems for studying special controls on which necessary optimality conditions degenerate. Illustrative examples are given.
Keywords: Volterra functional equation, distributed control system, optimal control problem, necessary optimality conditions, maximum principle, special control. 
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     author = {V. I. Sumin},
     title = {Volterra functional equations and optimization of distributed systems. {Special} optimal controls},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {53--76},
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     volume = {209},
     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/INTO_2022_209_a5/}
}
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V. I. Sumin. Volterra functional equations and optimization of distributed systems. Special optimal controls. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 2, Tome 209 (2022), pp. 53-76. http://geodesic.mathdoc.fr/item/INTO_2022_209_a5/