Abstract:
The paper shows the efficiency of the numerical algorithm for the class of problems that is considered by the example of optimal control, hard control, start control and hard starting control for the Leontieff type models. There are presented actual results of computational experiment. As the initial condition is used Showalter – Sidorov condition. This eliminates the restrictions caused by the need to initial checking the data that existed when using Cauchy conditions. The introduction presents various problems of optimal control. Is given their economic interpretation. The first section presents a theorem an existence of a unique solution the problem of optimal control, kind of exact and approximate solutions, the main stages of the algorithm for finding approximate solutions, theorem on the convergence of the approximate solution to the exact one. The second section presents the results of a computational experiment of solving the problem of optimal control. The third section presents the results of a computational experiment of solving the problem of hard control. The fourth section contains the results of numerical experiments solving the problem of start control and the problem of hard starting control. The fifth section presents the results of computational experiments with different parameters of the algorithm as an example a model of Leontieff type. It is shown that the change of parameters leads to small computational error, indicating the computational efficiency.
Keywords:
numerical solution, optimal control, Liontieff type models, computational effiency of the algorithm.
Citation:
A. V. Keller, “On the computational efficiency of the algorithm of the numerical solution of optimal control problems for models of Leontieff type”, J. Comp. Eng. Math., 2:2 (2015), 39–59
\Bibitem{Kel15}
\by A.~V.~Keller
\paper On the computational efficiency of the algorithm of the numerical solution of optimal control problems for models of Leontieff type
\jour J. Comp. Eng. Math.
\yr 2015
\vol 2
\issue 2
\pages 39--59
\mathnet{http://mi.mathnet.ru/jcem5}
\crossref{https://doi.org/10.14529/jcem150205}
\elib{https://elibrary.ru/item.asp?id=23885335}
Linking options:
https://www.mathnet.ru/eng/jcem5
https://www.mathnet.ru/eng/jcem/v2/i2/p39
This publication is cited in the following 15 articles:
M. A. Sagadeeva, “Zadacha optimalnogo dinamicheskogo izmereniya s multiplikativnym vozdeistviem v prostranstvakh differentsiruemykh «shumov»”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 28:4 (2024), 651–664
A. V. Keller, “O napravleniyakh issledovanii uravnenii sobolevskogo tipa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 16:4 (2023), 5–32
A. V. Keller, I. A. Kolesnikov, “Metody avtomaticheskogo i optimalnogo upravleniya v dinamicheskikh izmereniyakh”, J. Comp. Eng. Math., 10:4 (2023), 3–25
A. V. Keller, “Sistemy leontevskogo tipa i prikladnye zadachi”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 15:1 (2022), 23–42
E. V. Bychkov, S. A. Zagrebina, A. A. Zamyshlyaeva, A. V. Keller, N. A. Manakova, M. A. Sagadeeva, G. A. Sviridyuk, “Razvitie teorii optimalnykh dinamicheskikh izmerenii”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 15:3 (2022), 19–33
E. V. Bychkov, “Analytical study of the mathematical model of wave propagation in shallow water by the Galerkin method”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 14:1 (2021), 26–38
A. L. Shestakov, A. V. Keller, “Odnomernyi filtr Kalmana v algoritmakh chislennogo resheniya zadachi optimalnogo dinamicheskogo izmereniya”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 14:4 (2021), 120–125
M. A. Sagadeeva, O. V. Mitin, “Postroenie nablyudenii po dannym, iskazhennym pomekhami raznogo vida”, J. Comp. Eng. Math., 8:4 (2021), 9–16
A. L. Shestakov, S. A. Zagrebina, N. A. Manakova, M. A. Sagadeeva, G. A. Sviridyuk, “Numerical optimal measurement algorithm under distortions caused by inertia, resonances, and sensor degradation”, Autom. Remote Control, 82:1 (2021), 41–50
Manuel De la Sen, Asier Ibeas, Santiago Alonso-Quesada, “On the Reachability of a Feedback Controlled Leontief-Type Singular Model Involving Scheduled Production, Recycling and Non-Renewable Resources”, Mathematics, 9:17 (2021), 2175
J. Banasiak, N. A. Manakova, G. A. Sviridyuk, “Positive solutions to Sobolev type equations with relatively p-sectorial operators”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 13:2 (2020), 17–32
A O Kondyukov, T G Sukacheva, “Non-stationary model of incompressible viscoelastic Kelvin-Voigt fluid of higher order in the Earth's magnetic field”, J. Phys.: Conf. Ser., 1658:1 (2020), 012028
Alevtina V. Keller, Minzilia A. Sagadeeva, Springer Proceedings in Mathematics & Statistics, 325, Semigroups of Operators – Theory and Applications, 2020, 263
M. A. Sagadeeva, “Postroenie nablyudeniya dlya zadachi optimalnogo dinamicheskogo izmereniya po iskazhennym dannym”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 12:2 (2019), 82–96
A. O. Kondyukov, T. G. Sukacheva, “Fazovoe prostranstvo pervoi nachalno-kraevoi zadachi dlya sistemy Oskolkova vysshego poryadka”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 11:4 (2018), 67–77
Citation in format AMSBIB
Contact us: