Skip to main content
SpringerLink
Log in

Identification of the inputs of quasilinear systems

  • Estimation in Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Consideration was given to restoration of the input of the quasilinear dynamic system from the measurements of its output. By the input is meant the pair consisting of the initial system state and the input action on the system (control, perturbation, and so on). The problem was solved using A.N. Tikhonov’s method of regularization for which the sufficient convergence conditions and error estimates were established. Conditions for representability of an unknown input as a series in powers of a small parameter and the explicit form of the coefficients of this representation were determined.

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. Krasovskii, N.N., Teoriya upravleniya dvizheniem (Motion Control Theory), Moscow: Nauka, 1968.

    Google Scholar 

  2. Kurzhanskii, A.B., Upravlenie i nablyudenie v usloviyakh neopredelennosti (Control and Observation under Uncertainty), Moscow: Nauka, 1977.

    Google Scholar 

  3. Kryazhimskii, A.V. and Osipov, Yu.S., On Positional Modeling of Control in the Dynamic System, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1983, no. 2, pp. 51–60.

  4. Kirin, N.E., Metody posledovatel’nykh otsenok v zadachakh optimizatsii upravlyaemykh sistem (Methods of Successive Estimates in the Problems of Optimization of Controlled Systems), Leningrad: Leningr. Gos. Univ., 1975.

    Google Scholar 

  5. Gusev, M.I. and Kurzhanskii, A.B., Inverse Problems of Dynamics of Controlled Systems, in Mekhanika i nauchno-tekhnicheskii progress. T. 1. Obshchaya i prikladnaya mekhanika (Mechanics and Progress of Science and Technology. Vol. 1. General and Applied Mechanics), Moscow: Nauka, 1987.

    Google Scholar 

  6. Tikhonov, A.N. and Arsenin, V.Ya., Metody resheniya nekorrektnykh zadach (Methods to Solve Improperly Posed Problems), Moscow: Nauka, 1986.

    Google Scholar 

  7. Anikin, S.A. and Gusev, M.I., Estimation of the Disturbing Forces from the Motion Parameter Measurements, in Garantirovannoe otsenivanie i zadachi upravleniya (Guaranteed Estimation and Problems of Control), Sverdlovsk: UNTS AN SSSR, 1986.

    Google Scholar 

  8. Anikin, S.A., ON Estimation of Error of the A.N. Tikhonov Regularization Method in the Problem of Restoration of Inputs of Dynamic Systems, Zh. Vychisl. Mat. Mat. Fiz., 1997, no. 9, pp. 1056–1067.

  9. Subbotin, A.I., On Control of Motion of the Quasilinear System, Diff. Uravn., 1967, vol. III, no. 7, pp. 1114–1118.

    MathSciNet  Google Scholar 

  10. Al’brekht, E.G. and Ermolenko, E.A., Approximate Computation of the Optimal Processes in the Quasilinear Systems, Tekh. Kibernetika, 1994, no. 3, pp. 5–12.

  11. Vasil’ev, F.P., Chislennye metody resheniya ekstremal’nykh zadach (Numerical Methods for Solution of Extremal Problems), Moscow: Nauka, 1988.

    Google Scholar 

  12. Ioffe, A.D. and Tikhomirov, V.M., Teoriya ekstremal’nykh zadach (Theory of Extremal Problems), Moscow: Nauka, 1974.

    Google Scholar 

  13. Vainberg, M.M. and Trenogin, V.A., Teoriya vetvleniya reshenii nelineinykh uravnenii (Theory of Branching of Solutions of Nonlinear Equations), Moscow: Nauka, 1969.

    Google Scholar 

  14. Morozov, V.A., Regulyarnye metody resheniya nekorrektno postavlennykh zadach (Regular Methods of Solution of Improperly Posed Problems), Moscow: Nauka, 1987.

    MATH  Google Scholar 

  15. Bibikov, Yu.N., Kurs obyknovennykh differentsial’nykh uravnenii (Course of Ordinary Differential Equations), Moscow: Vysshaya Shkola, 1991.

    Google Scholar 

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

    Google Scholar 

  17. Fleming, W. and Rishel, R., Deterministic and Stochastic Optimal Control, New York: Springer, 1975. Translated under the title Optimal’noe upravlenie determinirovannymi i stokhasticheskimi sistemami, Moscow: Mir, 1978.

    MATH  Google Scholar 

  18. Trenogin, V.A., Funktsional’nyi analiz (Functional Analsis), Moscow: Nauka, 1980.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia

    S. A. Anikin

Authors
  1. S. A. Anikin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © S.A. Anikin, 2007, published in Avtomatika i Telemekhanika, 2007, No. 11, pp. 12–30.

This work was supported by the Russian Foundation for Basic Research, project no. 04-01-00148.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Anikin, S.A. Identification of the inputs of quasilinear systems. Autom Remote Control 68, 1900–1916 (2007). https://doi.org/10.1134/S0005117907110021

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117907110021

PACS number

Search

Navigation