Geodesic
On the solvability of the problem of synthesizing distributed and boundary controls in the optimization of oscillation processes
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 2, pp. 128-140

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We study the solvability of the problem of synthesis of distributed and boundary controls in the optimization of oscillation processes described by partial integro-differential equations with the Fredholm integral operator. Functions of external and boundary actions are nonlinear with respect to the controls. For the Bellman functional, an integro-differential equation of a specific form is obtained and the structure of its solution is found, which allows this equation to be represented as a system of two equations of a simpler form. An algorithm for constructing a solution to the problem of synthesizing distributed and boundary controls is described, and a procedure for finding the controls as a function (functional) of the state of the process is described.
Keywords: integro-differential equation, Fredholm operator, generalized solution, Bellman functional, Fréchet differential, optimal control synthesis. 
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     title = {On the solvability of the problem of synthesizing distributed and boundary controls in the optimization of oscillation processes},
     journal = {Trudy Instituta matematiki i mehaniki},
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     publisher = {mathdoc},
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     year = {2021},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2021_27_2_a10/}
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A. Kerimbekov. On the solvability of the problem of synthesizing distributed and boundary controls in the optimization of oscillation processes. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 2, pp. 128-140. http://geodesic.mathdoc.fr/item/TIMM_2021_27_2_a10/