Geodesic
Optimal boundary control for a distributed inhomogeneous oscillatory system with given intermediate conditions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 1, Tome 230 (2023), pp. 25-40.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we develop a constructive approach to the problem of optimal boundary control for a distributed inhomogeneous oscillatory system whose dynamics is modeled by a one-dimensional wave equation with piecewise constant characteristics. Using the approach proposed, one may satisfy multi-point intermediate conditions. The results obtained are illustrated by a specific example.
Mots-clés : oscillations
Keywords: optimal control, inhomogeneous process, wave equation, separation of variables 
@article{INTO_2023_230_a2,
     author = {V. R. Barseghyan and S. V. Solodusha},
     title = {Optimal boundary control for a distributed inhomogeneous oscillatory system with given intermediate conditions},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {25--40},
     publisher = {mathdoc},
     volume = {230},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_230_a2/}
}
TY  - JOUR
AU  - V. R. Barseghyan
AU  - S. V. Solodusha
TI  - Optimal boundary control for a distributed inhomogeneous oscillatory system with given intermediate conditions
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2023
SP  - 25
EP  - 40
VL  - 230
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2023_230_a2/
LA  - ru
ID  - INTO_2023_230_a2
ER  - 
%0 Journal Article
%A V. R. Barseghyan
%A S. V. Solodusha
%T Optimal boundary control for a distributed inhomogeneous oscillatory system with given intermediate conditions
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2023
%P 25-40
%V 230
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2023_230_a2/
%G ru
%F INTO_2023_230_a2
V. R. Barseghyan; S. V. Solodusha. Optimal boundary control for a distributed inhomogeneous oscillatory system with given intermediate conditions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 1, Tome 230 (2023), pp. 25-40. http://geodesic.mathdoc.fr/item/INTO_2023_230_a2/

[1] Barsegyan V. R., “Optimalnoe granichnoe upravlenie smescheniem na dvukh kontsakh pri kolebanii sterzhnya, sostoyaschego iz dvukh uchastkov raznoi plotnosti i uprugosti”, Differ. uravn. protsessy upravl., 2022, no. 2, 41–54 | Zbl

[2] Barsegyan V. R., Upravlenie sostavnykh dinamicheskikh sistem i sistem s mnogotochechnymi promezhutochnymi usloviyami, Nauka, M., 2016

[3] Butkovskii A. G., Metody upravleniya sistemami s raspredelennymi parametrami, Nauka, M., 1975

[4] Egorov A. I., Znamenskaya L. N., “Ob upravlyaemosti uprugikh kolebanii posledovatelno soedinennykh ob'ektov s raspredelennymi parametrami”, Tr. IMM UrO RAN., 17:1 (2011), 85–92

[5] Zvereva M. B., Naidyuk F. O., Zalukaeva Zh. O., “Modelirovanie kolebanii singulyarnoi struny”, Vestn. Voronezh. gos. un-ta. Ser. Fiz. Mat., 2014, no. 2, 111–119 | Zbl

[6] Zubov V. I., Lektsii po teorii upravleniya, Nauka, M., 1975

[7] Ilin V. A., “Optimizatsiya granichnogo upravleniya kolebaniyami sterzhnya, sostoyaschego iz dvukh raznorodnykh uchastkov”, Dokl. RAN., 440:2 (2011), 159–163 | Zbl

[8] Ilin V. A., “O privedenii v proizvolno zadannoe sostoyanie kolebanii pervonachalno pokoyaschegosya sterzhnya, sostoyaschego iz dvukh raznorodnykh uchastkov”, Dokl. RAN., 435:6 (2010), 732–735 | Zbl

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

[10] Kuleshov A. A., “Smeshannye zadachi dlya uravneniya prodolnykh kolebanii neodnorodnogo sterzhnya i uravneniya poperechnykh kolebanii neodnorodnoi struny, sostoyaschikh iz dvukh uchastkov raznoi plotnosti i uprugosti”, Dokl. RAN., 442:5 (2012), 594–597 | Zbl

[11] Lvova N. N., “Optimalnoe upravlenie nekotoroi raspredelennoi neodnorodnoi kolebatelnoi sistemoi”, Avtomat. telemekh., 1973, no. 10, 22–32 | Zbl

[12] Provotorov V. V., “Postroenie granichnykh upravlenii v zadache o gashenii kolebanii sistemy strun”, Vestn. Sankt-Peterburg. un-ta. Prikl. mat. Inform. Protsessy upravl., 2012, no. 1, 62–71

[13] Rogozhnikov A. M., “Issledovanie smeshannoi zadachi, opisyvayuschei protsess kolebanii sterzhnya, sostoyaschego iz neskolkikh uchastkov s proizvolnymi dlinami”, Dokl. RAN., 444 (2012), 488–491 | MR | Zbl

[14] Amara J. Ben, Beldi E., “Boundary controllability of two vibrating strings connected by a point mass with variable coefficients”, SIAM J. Control Optim., 57:5 (2019), 3360–3387 | DOI | MR | Zbl

[15] Amara J. Ben, Bouzidi H., “Null boundary controllability of a one-dimensional heat equation with an internal point mass and variable coefficients”, J. Math. Phys., 59:1 (2018), 1–22 | MR | Zbl

[16] Barseghyan V. R., “Control problem of string vibrations with inseparable multipoint conditions at intermediate points of time”, Mech. Solids., 54:8 (2019), 1216–1226 | DOI

[17] Barsegyan V. R., “The problem of optimal control of string vibrations”, Int. Appl. Mech., 56(4) (2020), 471–48 | DOI | MR

[18] Barseghian V. R., “String vibration observation problem”, Proc. 1 Int. Conf. “Control of Oscillations and Chaos” (Cat. No. 97TH8329), Vol. 2 (St. Petersburg, Russia, August 27-29, 1997), St. Petersburg, 1997, 309–310

[19] Barseghyan V. R., “The problem of boundary control of displacement at two ends by the process of oscillation of a rod consisting of two sections of different density and elasticity”, Mech. Solids., 58:2 (2023), 483–491 | DOI | MR | Zbl

[20] Barseghyan V. R., “Optimal boundary control of a distributed heterogeneous vibrating system with given states at intermediate times”, Comput. Math. Math. Phys., 62 (2022), 2023–2032 | DOI | MR | Zbl

[21] Barseghyan V. R., “On the controllability and observability of linear dynamic systems with variable structure”, Proc. Int. Conf. “Stability and Oscillations of Nonlinear Control Systems” (Pyatnitskiy's Conference) (Moscow, Russia, June 1-3, 2016), IEEE, 2016, 1–3

[22] Barseghyan V. R., “Control of stage by stage changing linear dynamic systems”, Yugoslav. J. Oper. Res., 22:1 (2012), 31–39 | DOI | MR | Zbl

[23] Barseghyan V. R., Barseghyan T. V., “On an approach to the problems of control of dynamic system with nonseparated multipoint intermediate conditions”, Automat. Remote Control., 76:4 (2015), 549–559 | DOI | MR | Zbl

[24] Barseghyan V., Solodusha S., “On the optimal control problem for vibrations of the rod/string consisting of two non-homogeneous sections with the condition at an intermediate time”, Mathematics., 10:23 (2022), 4444 | DOI

[25] Barseghyan V., Solodusha S., “Optimal boundary control of string vibrations with given shape of deflection at a certain moment of time”, Lect. Notes Comput. Sci., 12755 (2021), 299–313 | DOI | MR | Zbl

[26] Barseghyan V., Solodusha S., “On one problem in optimal boundary control for string vibrations with a given velocity of points at an intermediate moment of time”, Proc. Int. Russian Automation Conference (RusAutoCon) (Sochi, September 5-11, 2021), IEEE, 2021, 343–349 | MR

[27] Barseghyan V. R., Solodusha S. V., “On one boundary control problem of string vibrations with given velocity of points at an intermediate moment of time”, J. Phys. Conf. Ser., 2021 | MR

[28] Mercier D., Regnier V., “Boundary controllability of a chain of serially connected Euler–Bernoulli beams with interior masses”, Collect. Math., 60:3 (2009), 307–334 | DOI | MR | Zbl