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, FrДechet differential, optimal control synthesis
Received January 29, 2021
Revised March 22, 2021
Accepted April 2, 2021
Akylbek Kerimbekov, Dr. Phys.-Math. Sci., Prof., Kyrgyz-Russian Slavic university, Bishkek, 720022 Kyrgyzstan, e-mail: akl7@rambler.ru
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Cite this article as: A. Kerimbekov. On the solvability of the problem of synthesizing distributed and boundary controls in the optimization of oscillation processes, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, vol. 27, no. 2, pp. 128–140.
