Abstract:
We consider the problem of identifying the parameters of a dynamic system from a noisy history of measuring the phase trajectory. We propose a new approach to the solution based on the construction of an auxiliary optimal control problem such that its extremals approximate the measurement history with a given accuracy. Using the solutions of the corresponding characteristic system, we obtain estimates for the residual, which is the difference between the coordinates of the extremals and the measurements of the phase trajectory. An estimate for the result of identifying the parameters of the dynamic system is obtained. An illustrative numerical example is given.
Citation:
N. N. Subbotina, E. A. Krupennikov, “The method of characteristics in an identification problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 2, 2016, 255–266; Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 205–216
\Bibitem{SubKru16}
\by N.~N.~Subbotina, E.~A.~Krupennikov
\paper The method of characteristics in an identification problem
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 2
\pages 255--266
\mathnet{http://mi.mathnet.ru/timm1311}
\crossref{https://doi.org/10.21538/0134-4889-2016-22-2-255-266}
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\elib{https://elibrary.ru/item.asp?id=26040842}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2017
\vol 299
\issue , suppl. 1
\pages 205--216
\crossref{https://doi.org/10.1134/S008154381709022X}
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Linking options:
https://www.mathnet.ru/eng/timm1311
https://www.mathnet.ru/eng/timm/v22/i2/p255
This publication is cited in the following 11 articles:
N. N. Subbotina, E. A. Krupennikov, “Weak* Approximations to the Solution of a Dynamic Reconstruction Problem”, Proc. Steklov Inst. Math. (Suppl.), 317, suppl. 1 (2022), S142–S152
N. N. Subbotina, E. A. Krupennikov, “Weak* Solution to a Dynamic Reconstruction Problem”, Proc. Steklov Inst. Math., 315 (2021), 233–246
Vladimir Turetsky, “Two Inverse Problems Solution by Feedback Tracking Control”, Axioms, 10:3 (2021), 137
E. A. Krupennikov, “Properties of solutions of dynamic control reconstruction problems”, J. Phys.: Conf. Ser., 1864:1 (2021), 012034
Nina N. Subbotina, “On control reconstructions to management problems”, Contributions to Game Theory and Management, 13 (2020), 402–414
Evgenii Aleksandrovitch Krupennikov, Lecture Notes in Control and Information Sciences - Proceedings, Stability, Control and Differential Games, 2020, 239
Nina Subbotina, COMPUTATIONAL MECHANICS AND MODERN APPLIED SOFTWARE SYSTEMS (CMMASS'2019), 2181, COMPUTATIONAL MECHANICS AND MODERN APPLIED SOFTWARE SYSTEMS (CMMASS'2019), 2019, 020019
N. N. Subbotina, “Hamiltonian systems in dynamic reconstruction problems”, IFAC-PapersOnLine, 51:32 (2018), 136–140
E. A. Krupennikov, “A new approximate method for construction of the normal control”, IFAC-PapersOnLine, 51:32 (2018), 343–348
E. A. Krupennikov, “Solution of inverse problems for control systems with large control parameter dimension”, IFAC-PapersOnLine, 51:32 (2018), 434–438
Citation in format AMSBIB
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