Skip to main content
SpringerLink
Log in

Problems of boundary observability of elastic vibrations described by the system of telegrapher equations

  • Systems with Distributed Parameters
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Problems are solved for the observability of elastic vibrations described by various boundary problems for the system of telegrapher equations. The initial conditions that generate observable vibrations are found in the explicit form. The necessary time period of an observation is defined. The solutions of observation problems are given in the case of the classical and generalized solutions of the class L 2 of appropriate boundary problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Roitenberg, Ya.N., Avtomaticheskoe upravlenie (Automatic Control), Moscow: Nauka, 1978.

    Google Scholar 

  2. Lions, J.L., Controle optimal des systèmes gouvernés par équations aux derivées partielles, Paris: Dunod Gauthier-Villars, 1968. Translated under the title Optimal’noe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Moscow: Mir, 1972.

    MATH  Google Scholar 

  3. Lions, J.L., Exact Controllability, Stabilization and Perturbations for Distributed Systems, SIAM Rev., 1988, vol. 30, no. 1, pp. 1–68.

    Article  MATH  MathSciNet  Google Scholar 

  4. Vasil’ev, F.P., Kurzhanskii, M.A., and Potapov, M.M., The Straight-Line Method in Problems of Boundary Control and Boundary Observation for a String Vibration Equation, Vestn. Mosk. Gos. Univ., Vychisl. Mat. Kibern., 1993, no. 3, pp. 8–15.

  5. Znamenskaya, L.N., Zadacha granichnogo nablyudeniya za kolebaniyami struny. Programmnye sistemy: teoriya i prilozheniya (The Problem of Boundary Observation on Vibrations of the String. Program. Systems: Theory and Propositions), Moscow: Fizmatlit, 2004, vol. 2, pp. 331–347.

    Google Scholar 

  6. Snamenskaya, L.N., Controllability and Observability of Elastic Vibrations, Doctoral (Phys.-Math.) Dissertation, Pereslavl-Zalesskii: Inst. Prog. Sist., 2005.

    Google Scholar 

  7. Znamenskaya, L.N., Upravleniya uprugimi kolebaniyami (Control of Elastic Vibrations), Moscow: Fizmatlit, 2004.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalesskii, Russia

    L. N. Znamenskaya

  2. Moscow Aviation Institute, Moscow, Russia

    Z. E. Potapova

Authors
  1. L. N. Znamenskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Z. E. Potapova
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © L.N. Znamenskaya, Z.E. Potapova, 2007, published in Avtomatika i Telemekhanika, 2007, No. 2, pp. 103–112.

This work was supported by the Russian Foundation for Basic Research, project no. 06-01-00279 and by the Foundation for Russian Sciences Support.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Znamenskaya, L.N., Potapova, Z.E. Problems of boundary observability of elastic vibrations described by the system of telegrapher equations. Autom Remote Control 68, 303–312 (2007). https://doi.org/10.1134/S0005117907020105

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117907020105

PACS number

Search

Navigation