Geodesic
Synthesis of distributed optimal control in the tracking problem at the optimization of thermal processes described by integro-differential equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 183 (2020), pp. 85-97

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In this paper, we examine the synthesis problem for a distributed thermal control system in the case where a Fredholm integral operator is involved in the boundary-value problem. We use the method proposed by A. I. Egorov and develop it based on the Bellman scheme. Using the notions of a generalized solution of a boundary-value problem and the Frechet differential for the Bellman functional, we obtain a partial integro-differential equation. For synthesizing a distributed optimal control, we propose a numerical algorithm.
Keywords: generalized solution, Bellman functional, Fréchet differential, integro-differential equation, synthesis of optimal control. 
@article{INTO_2020_183_a7,
     author = {A. K. Kerimbekov},
     title = {Synthesis of distributed optimal control in the tracking problem at the optimization of thermal processes described by integro-differential equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {85--97},
     publisher = {mathdoc},
     volume = {183},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_183_a7/}
}
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A. K. Kerimbekov. Synthesis of distributed optimal control in the tracking problem at the optimization of thermal processes described by integro-differential equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 183 (2020), pp. 85-97. http://geodesic.mathdoc.fr/item/INTO_2020_183_a7/