Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

About History Editorial Page Addresses Scope Editorial Staff Submission Review For Authors Publication Ethics Issues Русская версия

A Problem of Control of Oscillations of a String with Non-separated Conditions on the Deflection Function in a Given Intermediate Moments of Time

Author(s):

Vanya Rafaelovich Barseghyan

Institute of Mechanics of National Academy of Sciences of RA
Yerevan State University

barseghyan@sci.am

Abstract:

The paper considers the problem of the control for the equations of oscillations of a string with given initial, final conditions and nonseparated values of deflection in the intermediate moments of time. The problem is solved by using the methods of separation of variables and the theory of control of finite-dimensional systems with nonseparated multipoint intermediate conditions. As an application of the proposed approach, an control action is constructed for the string oscillation with a given nonlocal value of the deflection of the string points at some two intermediate points of time.

Keywords

References:

  1. Butkovskii A. G. Control methods for systems with distributed parameters. Moscow, Nauka Publ, 1975. (In Russ. )
  2. Znamenskaya L. N. Control of elastic vibrations. Moscow, FIZMATLIT Publ, 2004. (In Russ. )
  3. Il'in V. A., Moiseev E. I. Optimization of boundary controls of string vibrations // Uspekhi Mat. Nauk. 2005. Vol. 60, № 6, P. 89-14. http://dx.doi.org/10.1070/RM2005v060n06ABEH004283
  4. Moiseev E. I., Kholomeeva A. A. On an optimal boundary control problem with a dynamic boundary condition // Differential Equations. 2013. № 49. P. 640-644
  5. Barseghyan V. R. About One Problem of Optimal Control of String Oscillations with Non-separated Multipoint Conditions at Intermediate Moments of Time // In: Tarasyev A., Maksimov V., Filippova T. (eds) Stability, Control and Differential Games. Lecture Notes in Control and Information Sciences - Proceedings. Springer, Cham. 2020. pp. 13-25. https://link.springer.com/chapter/10.1007/978-3-030-42831-0_2
  6. Barseghyan V. R. Optimal control of string vibrations with nonseparate state function conditions at given intermediate instants // Automation and Remote Control. 2020. Vol. 81, no. 2. P. 226-235. https://doi.org/10.1134/S0005117920020034
  7. Barsegyan V. R. The Problem of Optimal Control of String Vibrations // International Applied Mechanics. 2020. Vol. 56, № 4. P. 471-480. https://doi.org/10.1007/s10778-020-01030-w
  8. Barseghyan V. R. A control problem for string vibrations with nonseparated conditions on the velocities of deflection points at intermediate times, Trudy Instituta Matematiki i Mekhaniki URO RAN. 2019. Vol. 25, № 3. P. 24-33. DOI: 10. 21538/0134-4889-2019-25-3-24-33
  9. Barseghyan V. R., Saakyan M. A. The optimal control of wire vibration in the states of the given intermediate periods of time // Proceedings of NAS RA: Mechanics. 2008. no. 61(2). P. 52-60. (In Russ. )
  10. Barseghyan V. R. On the problem of boundary control of string oscillations with given states atintermediate moments of time // Proc. XIth All-Russian Congress on Basic Problems of Theoretical andApplied Mechanics (Kazan, August 20-24). 2015. Vol. 1. P. 354-356. (In Russ. )
  11. Aschepkov L. T. Optimal Control of the System with Intermediate Conditions // PMM. 2018. Vol. 45, № 2. P. 215-222. (In Russ. )
  12. Barseghyan V. R. Control of Compound Dynamic Systems and of Systems with Multipoint Intermediate Conditions. Moscow, Nauka Publ, 2016. (In Russ. )
  13. Barseghyan V. R., Barseghyan T. V. On an Approach to the Problems of Control of Dynamic System with Nonseparated Multipoint Intermediate Conditions // Automation and Remote Control. 2015. Vol. 76, № 4. P. 549-559. https://doi.org/10.1134/S0005117915040013
  14. Korzyuk V. I., Kozlovskaya I. S. () Two-point boundary problem for string oscillation equation with given velocity in arbitrary point of time. I // Proceedings of the Institute of Math. NAS of Belarus. 2010. no. 18(2). P. 22—35. (In Russ. )
  15. Korzyuk V. I., Kozlovskia I. S. Two-point boundary problem for the equation of string vibration with the given velocity at the certain moment of time. II // Proceedings of the Institute of Math. NAS of Belarus. 2011. no. 19(1). P. 62-70. (In Russ. )
  16. Makarov A. A., Levkin D. A. Multipoint boundary value problemfor pseudodierential equations in multilayer // Vistnyk of V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics. 2014. № 1120. Vol. 69. P. 64-74. (In Ukr. )
  17. Assanova A. T., Imanchiev A. E On the solvability of a nonlocal boundary value problem for a loadedhyperbolic equations with multi-point conditions // Bulletin of the Karaganda University. Series: Mathematics. 2016. № 1 (81). P. 15-20. (In Russ. )
  18. Bakirova E. A., Kadirbayeva Zh. M. On a Solvability of Linear Multipoint Boundary Value Problem for the Loaded Differential Equations // Izvestiya NAS RK. Ser. fiz. -mat. 2016. Vol. 5, № 309. P. 168-175. (In Russ. )
  19. Krasovsky N. N. The Theory of Motion Control. Moscow, Nauka Publ, 1968. (In Russ. )
  20. Zubov V. I. Lectures on Control Theory. Moscow, Nauka Publ, 1975. (In Russ. )

Full text (pdf)