Skip to main content
Log in

Necessary Optimality Conditions for a Nonlinear Problem of Control of Trajectory Bundles

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

This paper proves necessary maximin and maximax conditions for a control problem, when behavior of the object is described by a controllable differential inclusion with multivalued performance criterion.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. V. I. Zubov, Dynamics of Controlled Systems [in Russian], Vysshaya Shk., Moscow (1982).

    Google Scholar 

  2. D. A. Ovsyannikov, Mathematical Methods of Control of Bundles [in Russian], Izd. LGU, Leningrad (1980).

    Google Scholar 

  3. A. B. Kurzhanskii, Control and Observation under Conditions of Uncertainty [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  4. B. N. Bublik, F. G. Garashchenko, D. A. Ovsyannikov, and L. S. Sokolov, “An estimate of extreme values of an interval of initial phases and index of heterogeneity of a bundle in the linear accelerator of ions with drift tubes,” Preprint, 78-17, Kiev State Univ., Kiev (1977).

    Google Scholar 

  5. G. N. Konstantinov, Normalization of Actions on Dynamic Systems [in Russian], Izd. Irkutsk. Univ., Irkutsk (1983).

    Google Scholar 

  6. S. Otakulov, “Optimization problems for controlled differential inclusions,” Author's Abstracts for Doctoral Diss., TashGU, Tashkent (1993).

    Google Scholar 

  7. A. V. Plotnikov, “Study of some differential equations with multivalued right-hand sides,” Author's Abstracts of Doctoral Diss., YuUPU, Odessa (1994).

    Google Scholar 

  8. J. Warga, Optimal Control of Differential and Functional Equations [Russian translation], Nauka, Moscow (1977).

    Google Scholar 

  9. C. J. Himmelberg and F. S. Van Vieck, “Existence of solutions for generalized differential equations with unbounded right-hand side,” J. Diff. Eq., 61, 295-320 (1986).

    Google Scholar 

  10. A. A. Tolstonogov, Differential Inclusions in Banach Space [in Russian], Nauka, Novosibirsk (1986).

    Google Scholar 

  11. V. I. Blagodatskikh, “Maximum principle for differential inclusions,” in: Tr. MIAN SSSR, 166, 23-43 (1984).

    Google Scholar 

  12. A. I. Panasyuk and B. I. Panasyuk, Asymptotic Turnpike Optimization of Controlled Systems [in Russian], Nauka i Tekhnika, Minsk (1986).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Plotnikov, A.V. Necessary Optimality Conditions for a Nonlinear Problem of Control of Trajectory Bundles. Cybernetics and Systems Analysis 36, 729–733 (2000). https://doi.org/10.1023/A:1009432907531

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009432907531

Navigation