Skip to main content
SpringerLink
Log in

On the Method of Multivalent Guiding Functions for Periodic Solutions of Differential Inclusions

  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

The paper developed the method of multivalent vector guiding functions (MVGF). The notions of full collection of the strict MVGF's, full and sharp collection of the generalized MVGF's, and the regular MVGF were introduced and considered. These methods were extended to the problem of periodic trajectories of the controlled system obeying a differential inclusion.

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. Boltyanskii, V.G., Matematicheskie metody optimal'nogo upravleniya (MathematicalMethods of Optimal Control), Moscow: Nauka, 1969.

    Google Scholar 

  2. Borisovich, Yu.G., Gel'man, B.D., Myshkis, A.D., et al., Vvedenie v teoriyu mnogoznachnykh otobrazhenii (Introduction to the Theory of Multivalue Maps), Voronezh: Voronezh. Gos. Univ., 1986.

    Google Scholar 

  3. Górniewicz, L., Topological Fixed Point Theory of Multivalued Mappings, London: Kluwer, 1999.

    Google Scholar 

  4. Kamenskii, M., Obukhovskii, V., and Zecca, P., Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, New York: Walter de Gruyter, 2001.

    Google Scholar 

  5. Rachinskii, D.I., Forced Oscillations in the Control Systems in Close-to-Resonance Conditions, Avtom. Telemekh., 1995, no. 11, pp. 87-98.

    Google Scholar 

  6. Rachinskii, D.I., Rotating Guiding Functions for Periodic Systems with Delay, Proc. Int. Conf. Functional Diferential Equations &; Appl., Moscow, August 14-21, 1994, p. 68.

  7. Rachinskii, D.I., Multivalent Guiding Functions in Forced Oscillation Problems, Nonlinear Anal. Theory, Methods Appl., 1996, vol. 26, no.3, pp. 631-639.

    Google Scholar 

  8. Krasnosel'skii, M.A., Operator sdviga po traectoriyam differentsial'nykh uravnenii, Moscow: Nauka, 1966. Translated under the title The Operator of Translation Along the Trajectories of Differential Equations, in: “Translation of Mathematical Monographs,” Providence: American Mathematical Society, 1968, vol. 19.

    Google Scholar 

  9. Krasnoselskii, A.M., Krasnoselskii, M.A., Mawhin, J., et al., Generalized Guiding Functions in a Problem on High Frequency Forced Oscillations, Nonlinear Anal. Theory, Methods Appl., 1994, vol. 22, no.11, pp. 1357-1371.

    Google Scholar 

  10. Krasnosel'skii, M.A. and Zabreiko, P.P., Geometricheskie metody nelineinogo analiza (Geometrical Methods of Nonlinear Analysis), Moscow: Nauka, 1975. Translated under the title Geometrical Methods of Nonlinear Analysis, Berlin: Springer, 1984, vol. 263.

    Google Scholar 

  11. Deimling, K., Multivalued Differential Equations, New York: Walter de Gruyter, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Voronezh State Pedagogical University, Voronezh, Russia

    S. V. Kornev

Authors
  1. S. V. Kornev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kornev, S.V. On the Method of Multivalent Guiding Functions for Periodic Solutions of Differential Inclusions. Automation and Remote Control 64, 409–419 (2003). https://doi.org/10.1023/A:1023261508119

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1023261508119

Keywords

Search

Navigation