Interpolation approach in problems of modeling dynamic systems with ellipsoid parameter estimations

DOI: 10.34759/trd-2022-124-24

Аuthors

Morozov A. Y.

Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, 44-2, Vavilova str., Moscow, 119333, Russia

e-mail: morozov@infway.ru

Keywords:

ellipsoid estimates, adaptive interpolation algorithm, interval system of ordinary differential equations

References

1. Moore R.E., Kearfott R.B., Cloud M.J. Introduction to Interval Analysis, SIAM, 2009, 223 p.
2. Dobronets B.S. Interval’naya matematika (Interval mathematics), Krasnoyarsk, Krasnoyarskii gosudarstvennyi universitet, 2007, 218 p.
3. Sharyi S.P. Konechnomernyi interval’nyi analiz (Finite-dimensional interval analysis), Novosibirsk, Izd-vo XYZ, 2017, 618 p.
4. Morozov A.Yu., Reviznikov D.L. Trudy MAI, 2016, no. 89. URL: http://trudymai.ru/eng/published.php?ID=73407
5. Chernous’ko F.L. Otsenivanie fazovykh sostoyanii dinamicheskikh sistem. Metod ellipsoidov (Estimation of phase states of dynamical systems. Ellipsoid method), Moscow, Nauka, 1988, 319 p.
6. Kurzhanski A.V., Vdlyi I. Ellipsoidal Calculus for Estimation and Control, SCFA, Boston, 1997. DOI:10.1007/978-1-4612-0277-6
7. Fu C., Ren X., Yang Y.-F., Lu K., Qin W. Steady-state response analysis of cracked rotors with uncertain but bounded parameters using a polynomial surrogate method, Communications in Nonlinear Science and Numerical Simulation, 2019, no. 68, pp. 240–256. DOI: 10.1016/j.cnsns.2018.08.004
8. Fu C., Xu Y., Yang Y., Lu K., Gu F., Ball A. Response analysis of an accelerating unbalanced rotating system with both random and interval variables, Journal of Sound and Vibration, 2020, no. 466, pp. 115047. DOI:10.1016/j.jsv.2019.115047
9. Berz M., Makino K. Verified integration of ODEs and flows with differential algebraic methods on Taylor models, Reliable Computing, 1998, vol. 4, no. 4, pp. 361–369.
10. Rogalev A.N. Vychislitel’nye tekhnologii, 2003, vol. 8, no. 5, pp. 102–116.
11. Ermakov S.M., Mikhailov G.A. Statisticheskoe modelirovanie (Statistical modeling), Moscow, Nauka, 1982, 296 p.
12. Morozov A.Yu., Reviznikov D.L. Differentsial’nye uravneniya, 2021, vol. 57, no. 7, pp. 976–987. DOI: 10.31857/S0374064121070104
13. Gidaspov V.Yu., Morozov A.Yu., Reviznikov D.L. Zhurnal vychislitel’noi matematiki i matematicheskoi fiziki, 2021, vol. 61, no. 9, pp. 1416–1430. DOI: 10.31857/S0044466921090106
14. Oseledets I.V. Tensor-train decomposition, SIAM Journal on Scientific Computing, 2011, vol. 33, no 5, pp. 2295–2317. DOI: 10.1137/090752286
15. Oseledets I., Tyrtyshnikov E. TT-cross approximation for multidimensional arrays, Linear Algebra and its Applications, 2010, vol. 432, no. 1, pp. 70–88. DOI: 10.1016/j.laa.2009.07.024
16. Oseledets I.V. Tenzornye metody i ikh primenenie (Tensor methods and their applications), Dissertation of Doctor of Physical and Mathematical Sciences, Moscow, M.: Institut vychislitel’noi matematiki RAN, 2009, 282 p.
17. Smolyak S.A. Doklady AN SSSR, 1963, vol. 148, no. 5, pp. 1042-1045.
18. Bungatrz H-J., Griebel M. Sparse grids, Acta Numerica, 2004, vol. 13, no. 1. pp. 147–269.
19. Gerstner T., Griebel M. Sparse grids, Encyclopedia of Quantitative Finance, New York, 2010.
20. Morozov A.Yu. Programmnaya inzheneriya, 2021, vol. 12, no. 8, pp. 395–403. DOI: 10.17587/prin.12.395-403.
21. OpenMP. URL: https://www.openmp.org/
22. Morozov A.Yu. Trudy MAI, 2022, no. 123. URL: https://trudymai.ru/eng/published.php?ID=165501. DOI: 10.34759/trd-2022-123-14
23. Gidaspov V.Yu., Moskalenko O.A. Trudy MAI, 2016, no. 90. URL: http://trudymai.ru/eng/published.php?ID=74647
24. Gidaspov V.Yu., Kononov D.S. Trudy MAI, 2019, no. 109. URL: http://trudymai.ru/eng/published.php?ID=111353. DOI: 10.34759/trd-2019-109-6
25. Kryukov V.G., Abdullin A.L., Nikandrova M.V., Iskhakova R.L. Trudy MAI, 2019, no. 105. URL: http://trudymai.ru/eng/published.php?ID=104166

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