The problem of modeling a solution is studied for a nonlinear system of differential equations with constant delay, inexactly known right-hand side, and inaccurately given initial state. The case is considered when the right side of the system is a nonsmooth (it is only known that it is Lebesgue measurable) unbounded function (belonging to the space of square integrable functions in the Euclidean norm). An algorithm for solving this system that is stable to information noise and calculation errors is constructed. The algorithm is based on the concepts of feedback control theory. An estimate of the convergence rate of the algorithm is established. The possibility of using the algorithm to find an approximate solution to a system of ordinary differential equations is mentioned.
Keywords: system with delay, approximate solution
Received March 20, 2024
Revised April 11, 2024
Accepted April 15, 2024
Funding Agency: The work was performed as part of research conducted in the Ural Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Agreement number 075-02-2024-1377).
Marina Sergeevna Blizorukova, Cand. Sci. (Phys.-Math.), Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia, e-mail: msb@imm.uran.ru
Vyacheslav Ivanovich Maksimov, Dr. Phys.-Math. Sci., Prof., Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia, e-mail: maksimov@imm.uran.ru
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Cite this article as: M.S. Blizorukova, V.I. Maksimov. On modeling a solution of systems with constant delay using controlled models. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2024, vol. 30, no. 2, pp. 39–49. Proceedings of the Steklov Institute of Mathematics, 2024, Vol. 325, Suppl. 1, pp. S48–S57.
