Siberian Mathematical Journal

, Volume 35, Issue 1, pp 65–76 | Cite as

The variational maximum principle and second-order optimality conditions for impulse processes and singular processes

  • V. A. Dykhta


Optimality Condition Maximum Principle Variational Maximum Singular Process Impulse Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. I. Gurman, V. A. Dykhta, and G. A. Kolokol'nikova, “Nonlocal transformations of degenerated optimal control problems and impulse modes,” submitted to VINITI on June 15, 1990, No. 3455-V90.Google Scholar
  2. 2.
    V. A. Dykhta, “Impulse-trajectory extension of degenerated optimal control problems,” IMACS Ann. Comput. Appl. Math.,8, 103–109 (1990).Google Scholar
  3. 3.
    S. T. Zavalishchin and A. N Sesekin, Impulse Processes: Models and Applications [in Russian], Nauka, Moscow (1991).Google Scholar
  4. 4.
    E. S. Levitin, A. A. Milyutin, and N. P. Osmolovskii, “Higher-order conditions for a local minimum in problems with constraints,” Uspekhi Mat. Nauk,38, No. 6, 85–148 (1978).Google Scholar
  5. 5.
    V. A. Dykhta, “Conditions of a local minimum for singular modes in systems with linear control,” Avtomat. i Telemekh., No. 2, 5–10 (1981).Google Scholar
  6. 6.
    S. T. Zavalishchin, “Special nonlinear differential equations in generalized functions,” Differentsial'nye Uravneniya,26, No. 8, 1316–1323 (1990).Google Scholar
  7. 7.
    A. P. Afanas'ev, V. V. Dikusar, A. A. Milyutin, and S. A. Chukanov, Necessary Conditions in Optimal Control [in Russian], Nauka, Moscow (1990).Google Scholar
  8. 8.
    N. P. Osmolovskii, “Necessary and sufficient higher-order conditions for Pontryagin and bounded-strong minima in the optimal control problem,” Dokl. Akad. Nauk SSSR,323, No. 5, 1052–1056 (1988).Google Scholar
  9. 9.
    N. P. Osmolovskii, “Necessary and sufficient higher-orders conditions in the optimal control problem. I,” submitted to VINITI on April 1, 1986, No. 2190-V86; II: submitted to VINITI on April 1, 1986, No. 2191-V86.Google Scholar
  10. 10.
    V. A. Dykhta, G. A. Kolokol'nikova, and I. A. Nikiforova, “Nonlocal transformations of optimal control problems and minimum conditions on the set of sequences in problems with singular modes,” in: Theoretical and Applied Problems of Optimal Control [in Russian], Nauka, Novosibirsk, 1985, pp. 59–75.Google Scholar
  11. 11.
    A. V. Dmitruk, “Second-order conditions for the Pontryagin minimum in the optimal control problem with linear control input,” Izv. Akad. Nauk SSSR Ser. Mat.,50, No. 2, 284–312 (1986).Google Scholar
  12. 12.
    I. A. Nikiforova, Second-Order Optimality Conditions for Impulse Modes [in Russian], Diss. Kand. Fiz.-Mat. Nauk, Irkutsk. Univ., Irkutsk (1990).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • V. A. Dykhta
    • 1
  1. 1.Irkutsk

Personalised recommendations