Geodesic
Thermoelastic strip-shaped plate motion control: optimal restoration of deflection from incomplete measurements with errors
Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 30 (2014) no. 30, pp. 64-74 
V. R. Barseghyan. Thermoelastic strip-shaped plate motion control: optimal restoration of deflection from incomplete measurements with errors. Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 30 (2014) no. 30, pp. 64-74. http://geodesic.mathdoc.fr/item/TSP_2014_30_30_a2/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider a problem of motion control for a thermoelastic strip-shaped plate, namely, the problem of optimal restoration of its deflection in the presence of errors in temperature measurements. By the separation of variables, this problem is reduced to a problem for an infinite system of ordinary differential equations involving real signal observation. For each harmonic, using the incoming signal boost, we construct a universal optimal operation that allows us to restore the plate’s deflection at any of its points and at any time instant.

[1] Korotkii A. I., “Obratnye zadachi dinamiki upravlyaemykh sistem s raspredelennymi parametrami”, Izv. vyssh. ucheb. zavedenii. Matematika, 1995, no. 11, 101–124

[2] Degtyarev G. L., Sirazetdinov T. K., “Sintez optimalnogo upravleniya v sistemakh s raspredelennymi parametrami pri nepolnom izmerenii sostoyaniya (obzor)”, Izv. AN SSSR. Kibernetika, 1983, no. 2, 123–136

[3] Barseghyan V. R., “String vibration observation problem”, 1st Int. Conf. Control of Oscillations and Chaos (St. Petersburg, 1997), v. 2, 309–310

[4] Barsegyan V. R., Airapetyan V. V., “K zadache nablyudeniya upravlyaemykh kolebatelnykh dvizhenii membrany”, Uchen. zapiski EGU, 2 (1997), 21–26

[5] Barsegyan V. R., “Zadacha optimalnogo vosstanovleniya sostoyaniya sistem s raspredelennymi parametrami pri nalichii pogreshnostei v nepolnykh izmereniyakh”, Izv. NAN RA, Mekhanika, 57:1 (2004), 70–75 | MR

[6] Movsisyan L. A., Gabrielyan M. S., “Ob odnoi zadache upravleniya dvizheniem termouprugoi plastinki-polosy”, Izv. NAN RA, Mekhanika, 48:3 (1995), 15–22 | MR

[7] Novatskii V., Dinamicheskie zadachi termouprugosti, Mir, M., 1970

[8] Bolotin V. V., “Uravnenie nestatsionarnykh temperaturnykh polei v tonkikh obolochkakh pri nalichii istochnikov tepla”, PMM, 24:2 (1960), 361–363 | Zbl

[9] Krasovskii N. N., Teoriya upravleniya dvizheniem, Nauka, M., 1968 | MR

[10] Kurzhanskii A. B., Upravlenie i nablyudenie v usloviyakh neopredelennosti, Nauka, M., 1977 | MR