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Izv. RAN. Ser. Mat., 2000, Volume 64, Issue 4, Pages 163–182 (Mi izv299)  

This article is cited in 6 scientific papers (total in 6 papers)

A theorem of existence of an optimal control for the Goursat–Darboux problem without convexity assumptions

A. A. Tolstonogov

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

Abstract: We prove a theorem on the existence of solutions of the minimization problem for the integral functional on solutions of the controlled system described by the Goursat–Darboux equation, which is linear with respect to the phase variables and their derivatives, with constraints on the control, the phase variables, and their first partial derivatives.
The system is controlled by means of boundary and distributed controls. We do not assume that the functional to be minimized is convex with respect to the controls. The sets of admissible controls and the constraints on the phase variables and their first partial derivatives also are non-convex.

DOI: https://doi.org/10.4213/im299

Full text: PDF file (1527 kB)
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English version:
Izvestiya: Mathematics, 2000, 64:4, 807–826

Bibliographic databases:

MSC: 28B20, 54C60, 54C65, 54C50, 54C08, 47D06, 47D03
Received: 13.04.1999

Citation: A. A. Tolstonogov, “A theorem of existence of an optimal control for the Goursat–Darboux problem without convexity assumptions”, Izv. RAN. Ser. Mat., 64:4 (2000), 163–182; Izv. Math., 64:4 (2000), 807–826

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Tolstonogov, “Existence of an optimal control without convexity assumptions in a first-order evolution system”, Sb. Math., 192:9 (2001), 1381–1398  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Lisachenko I.V., Sumin V.I., “Nelineinaya upravlyaemaya zadacha Gursa–Darbu: usloviya sokhraneniya razreshimosti «v tselom»”, Vestn. Tambovskogo un-ta. Ser.: Estestvennye i tekhnicheskie nauki, 14:4 (2009), 736–737  elib
    3. I. V. Lisachenko, V. I. Sumin, “Printsip maksimuma dlya terminalnoi zadachi optimizatsii sistemy Gursa–Darbu v klasse funktsii s summiruemoi smeshannoi proizvodnoi”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 2, 52–67  mathnet  elib
    4. Lisachenko I.V., Sumin V.I., “Nonlinear Goursat-Darboux Control Problem: Conditions for the Preservation of Global Solvability”, Differ Equ, 47:6 (2011), 863–876  crossref  mathscinet  zmath  isi  elib  elib  scopus
    5. Lisachenko I.V., “Neobkhodimye usloviya optimalnosti dlya terminalnoi zadachi optimizatsii sistemy gursa-darbu v klasse funktsii s summiruemoi smeshannoi proizvodnoi”, Vestnik nizhegorodskogo universiteta im. N.I. Lobachevskogo, 2011, no. 3-2, 115–120  elib
    6. Mamehrashi K., Yousefi S.A., Soltanian F., “On the Numerical Scheme of a 2D Optimal Control Problem With the Hyperbolic System Via Bernstein Polynomial Basis”, Trans. Inst. Meas. Control, 41:7 (2019), 1896–1903  crossref  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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