mathnasТруды Института математики НАН БеларусиProceedings of the Institute of Mathematics of the NAS of Belarus1812-5093Институт математики НАН Беларуси10.67268/1812-5093-2026-34-1s-15-31RYYHQGmathnas-182Research ArticleВЕЩЕСТВЕННЫЙ, КОМПЛЕКСНЫЙ И ФУНКЦИОНАЛЬНЫЙ АНАЛИЗREAL, COMPLEX AND FUNCTIONAL ANALYSISЗадачи оптимизации для непрерывных 2D систем управленияOptimization problems for 2D continuous control systemsДымковМ. П.DymkovM. P.

Минск

Minsk

dymkov_m@bseu.byДымковВ. М.DymkouV. M.

Минск

Minsk

udymkov@mail.ruБелорусский государственный экономический университетБеларусьBelarusian State Economic UniversityBelarus202607112026341s1531Copyright © Дымков М.П., Дымков В.М., 20262026Дымков М.П., Дымков В.М.Dymkov M.P., Dymkou V.M.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://mathnas.ejournal.by/jour/article/view/182

В статье представлено обобщение дискретных 2D систем Россера и Форназини–Маркезини на непрерывный случай. Получены формулы для представления решений линейных непрерывных $2\mathrm{D}$ систем, в том числе указана возможность расширения методов операционного исчисления путем построения соответствующих интегральных преобразований по пространственной переменной. Рассмотрены линейно-квадратичные задачи оптимизации, для которых получены соответствующие условия оптимальности и форма представления оптимального управления.

The paper presents an extension of discrete $2\mathrm{D}$ systems of Roesser and Fornasini–Marchesini types for the continuous case. Formulas for solution representation of linear continuous $2\mathrm{D}$ systems are obtained, including the possibility of expanding the methods of operational calculus by constructing corresponding integral transformations with respect to the spatial variable. Some linear-quadratic optimization problems are considered and the corresponding optimality conditions based on the operator setting are stated. Also, some form of the optimal control representation is presented.

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The authors declare that there are no conflicts of interest present.