Geodesic
On modeling a solution of systems with constant delay using controlled models
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 2, pp. 39-49 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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M. S. Blizorukova; V. I. Maksimov. On modeling a solution of systems with constant delay using controlled models. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 2, pp. 39-49. http://geodesic.mathdoc.fr/item/TIMM_2024_30_2_a2/

[1] Osipov Yu.S., Kryazhimskii A.V., “O dinamicheskom reshenii operatornykh uravnenii”, Dokl. AN SSSR, 269:3 (1983), 552–556 | MR | Zbl

[2] Osipov Yu.S., Kryazhimskii A.V., “O modelirovanii parametrov dinamicheskoi sistemy”, Zadachi upravleniya i modelirovaniya v dinamicheskikh sistemakh, sb. statei, Izd-vo Ural. nauch. tsentra, Sverdlovsk, 1984, 47–68

[3] Kryazhimskii A.V., Maksimov V.I., Osipov Yu.S., “O modelirovanii upravleniya v dinamicheskikh sistemakh”, Prikl. matematika i mekhanika, 47:6 (1983), 883–890 | MR

[4] Kryazhimskii A.V., Osipov Yu.S., “O nailuchshem priblizhenii operatora differentsirovaniya v klasse neuprezhdayuschikh operatorov”, Mat. zametki, 37:2 (1985), 192–199 | MR | Zbl

[5] Osipov Yu.S., Kryazhimskii A.V., “Metod funktsii Lyapunova v zadache modelirovaniya dvizheniya”, Ustoichivost dvizheniya, sb. tr., Nauka, Novosibirsk, 1985, 53–56

[6] Krasovskii N.N., Subbotin A.I., Pozitsionnye differentsialnye igry, Nauka, M., 1974, 456 pp. | MR

[7] Maksimov V.I., “Pozitsionnoe modelirovanie upravlenii i nachalnykh funktsii dlya sistem Volterra”, Differents. uravneniya, 23:4 (1987), 618–629 | MR

[8] Maksimov V.I., “Chislennyi metod nakhozhdeniya priblizhennykh reshenii parabolicheskikh variatsionnykh neravenstv”, Differents. uravneniya, 24:11 (1988), 1994–2004 | MR

[9] Maksimov V., “The method of extremal shift in control problems for evolution variational inequalities under uncertainty”, Evol. Equ. Control The, 11:4 (2022), 1373–1398 | DOI | MR | Zbl

[10] Maksimov V.I., “O suschestvovanii silnykh reshenii differentsialnykh uravnenii v gilbertovom prostranstve”, Differents. uravneniya, 24:3 (1988), 618–629

[11] Osipov Yu.S., Kryazhimskii A.V., Inverse problems for ordinary differential equations: dynamical solutions, Gordon and Breach, 1995, 625 pp. | MR | Zbl

[12] Banks H.T., “Approximation of nonlinear functional–differential systems”, J. Optim. Theory Appl., 29 (1979), 383–408 | DOI | MR | Zbl

[13] Kappel F., Schappaher W., “Non-linear functional differential equations and abstract integral equations”, Proc. Roy. Soc. Edinburgh, 84:1–2 (1979), 71–91 | DOI | MR | Zbl

[14] Jackiewicz Z., “The numerical solutions of Volterra functional differential equations of neutral type”, SIAM J. Numer. Analysis, 18:4 (1981), 615–626 | DOI | MR | Zbl

[15] Ito K., Kappel F., “Approximation of infinite delay and Volterra type equations”, Numer. Math., 54 (1989), 405–444 | DOI | MR | Zbl

[16] Lasiecka I., Manitius A., “Differentiability and convergence rates of approximating semigroups for retarded functional differential equations”, SIAM J. Numer. Analysis, 25:4 (1988), 883–907 | DOI | MR | Zbl

[17] Maksimov V.I., “Ob otslezhivanii traektorii dinamicheskoi sistemy”, Prikl. matematika i mekhanika, 75:6 (2011), 951–960 | MR | Zbl