Geodesic
On the solution of inverse problems of dynamics of linearly controlled systems by the negative discrepancy method
Informatics and Automation, Optimal control, Tome 291 (2015), pp. 266-275.

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The paper is devoted to the substantiation of the negative discrepancy method for solving inverse problems of the dynamics of deterministic control systems that are nonlinear in state variables and linear in control. The problem statements include the known sampling history of trajectories measured inaccurately, with known error estimates. The investigation is based on the Pontryagin maximum principle. The results of simulation of an inverse problem for a macroeconomic model are presented. 
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N. N. Subbotina; T. B. Tokmantsev; E. A. Krupennikov. On the solution of inverse problems of dynamics of linearly controlled systems by the negative discrepancy method. Informatics and Automation, Optimal control, Tome 291 (2015), pp. 266-275. http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a19/

[1] Albrekht E.G., “Metodika postroeniya i identifikatsii matematicheskikh modelei makroekonomicheskikh protsessov”, Statya 5, Issledovano v Rossii: Elektron. zhurn., 2002, 54–86

[2] Bellman R., Dynamic programming, Princeton Univ. Press, Princeton, NJ, 1957 | MR | Zbl

[3] Klark F., Optimizatsiya i negladkii analiz, Nauka, M., 1988 | MR

[4] Krasovskii N.N., Teoriya upravleniya dvizheniem: Lineinye sistemy, Nauka, M., 1968 | MR

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

[6] Krupennikov E.A., “K obosnovaniyu metoda resheniya zadachi rekonstruktsii dinamiki makroekonomicheskoi modeli”, Tr. In-ta matematiki i mekhaniki UrO RAN, 21:2 (2015), 102–114

[7] Kryazhimskii A.V., Osipov Yu.S., “O modelirovanii upravleniya v dinamicheskoi sisteme”, Izv. AN SSSR. Ser. tekhn. kibern., 1983, no. 2, 51–60 | MR

[8] Osipov Yu.S., Kryazhimskii A.V., Inverse problems for ordinary differential equations: Dynamical solutions, Gordon and Breach, Amsterdam, 1995 | MR | Zbl

[9] Li E.B., Markus L., Osnovy teorii optimalnogo upravleniya, Nauka, M., 1972 | MR

[10] Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V., Mischenko E.F., Matematicheskaya teoriya optimalnykh protsessov, Fizmatgiz, M., 1961

[11] Subbotin A.I., Obobschennye resheniya uravnenii v chastnykh proizvodnykh pervogo poryadka: Perspektivy dinamicheskoi optimizatsii, In-t kompyut. issled., M.; Izhevsk, 2003

[12] Subbotina N.N., Kolpakova E.A., Tokmantsev T.B., Shagalova L.G, Metod kharakteristik dlya uravneniya Gamiltona–Yakobi–Bellmana, RIO UrO RAN, Ekaterinburg, 2013

[13] Subbotina N.N., Tokmantsev T.B., “Klassicheskie kharakteristiki uravneniya Bellmana v konstruktsiyakh setochnogo optimalnogo sinteza”, Tr. MIAN, 271 (2010), 259–277 | MR | Zbl

[14] Subbotina N.N., Tokmantsev T.B., “The method of characteristics in inverse problems of dynamics”, Univers. J. Control Autom., 1:1 (2013), 79–85

[15] Subbotina N.N., Tokmantsev T.B., “Issledovanie ustoichivosti resheniya obratnykh zadach dinamiki upravlyaemykh sistem po otnosheniyu k vozmuscheniyam vkhodnykh dannykh”, Tr. In-ta matematiki i mekhaniki UrO RAN, 20:3 (2014), 218–233 | MR

[16] Subbotina N.N., Tokmantsev T.B., “Optimal synthesis to inverse problems of dynamics”, Proc. 19th IFAC World Congr., 2014, Int. Fed. Autom. Control, Laxenburg, 2014, 5866–5871

[17] Tikhonov A.N., “O reshenii nekorrektno postavlennykh zadach i metode regulyarizatsii”, DAN SSSR, 151:3 (1963), 501–504 | MR | Zbl

[18] Tikhonov A.N., “O regulyarizatsii nekorrektno postavlennykh zadach”, DAN SSSR, 153:1 (1963), 49–52 | MR | Zbl