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Sbornik: Mathematics, 2001, Volume 192, Issue 9, Pages 1381–1398
DOI: https://doi.org/10.1070/SM2001v192n09ABEH000597 (Mi sm597) 		 
Existence of an optimal control without convexity assumptions in a first-order evolution system

A. A. Tolstonogov

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences
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DOI: https://doi.org/10.1070/SM2001v192n09ABEH000597
Abstract: An existence theorem is proved for an optimal control problem with constraints that is described by a first-order linear evolution equation, without the usual convexity assumptions relating to the control. The result is obtained by using properties of a multivalued integral and quasi-concavity conditions relating to the state variable. An example of a parabolic control system is treated at length.
Received: 27.09.2000
Russian version:
Matematicheskii Sbornik, 2001, Volume 192, Number 9, Pages 125–142
DOI: https://doi.org/10.4213/sm597
Bibliographic databases:
UDC: 517.97
MSC: Primary 49J15, 34H05; Secondary 49J45, 49J20, 93C15
Language: English
Original paper language: Russian
Citation: A. A. Tolstonogov, “Existence of an optimal control without convexity assumptions in a first-order evolution system”, Mat. Sb., 192:9 (2001), 125–142; Sb. Math., 192:9 (2001), 1381–1398
Citation in format AMSBIB
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    Russian version PDF:217
    English version PDF:16
    References:56
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