Geodesic
A nonlinear identification problem
Trudy Instituta matematiki i mehaniki, Tome 23 (2017) no. 1, pp. 206-211 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a nonlinear dynamic system with an unknown vector parameter in its description. An observer can calculate the phase vector of this system on the interval $[0,T]$ with an error whose modulus does not exceed a small value $h>0$. This information on the dynamics of the system should be used to find the unknown vector. We obtain constructive sufficient conditions under which it is possible to restore the unknown vector with decreasing error as the value of $h$ tends to zero. It turns out that it is sufficient to use discrete measurements of the output of the system.
Mots-clés : identification
Keywords: dynamic systems, inverse problems. 
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M. S. Nikol'skii. A nonlinear identification problem. Trudy Instituta matematiki i mehaniki, Tome 23 (2017) no. 1, pp. 206-211. http://geodesic.mathdoc.fr/item/TIMM_2017_23_1_a19/

[1] Gabasov R., Kirillova F., Kachestvennaya teoriya optimalnykh protsessov, Nauka, M., 1971, 508 pp.

[2] Grop D., Metody identifikatsii sistem, Mir, M., 1979, 302 pp.

[3] Kurzhanskii A.B., “Zadacha identifikatsii - teoriya garantirovannykh otsenok”, Avtomatika i telemekhanika, 1991, no. 4, 3–26

[4] Osipov Yu.S., Vasilev F.P., Potapov M.M., Osnovy metoda dinamicheskoi regulyarizatsii, Izd-vo Mosk. un-ta, M., 1999, 238 pp.

[5] L.S. Pontryagin [i dr.], Matematicheskaya teoriya optimalnykh protsessov, Fizmatgiz, M., 1961, 391 pp.

[6] Li E.B., Markus L., Osnovy teorii optimalnogo upravleniya, Nauka, M., 1972, 576 pp.

[7] Gantmakher F.R., Teoriya matrits, Nauka, M., 1966, 576 pp. | MR