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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2001, Volume 233, Pages 95–124 (Mi tm227)  
This article is cited in 2 scientific papers (total in 2 papers)

Asymptotics of Optimal Synthesis for One Class of Extremal Problems

M. I. Zelikin, L. F. Zelikina, R. Hildebrand
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Abstract: The asymptotics of an optimal control while approaching the origin is found for a class of mean square deviation minimization problems with a unilateral force. The asymptotics is described by a series of impulses of maximal amplitude that decrease in time and have the support in the neighborhoods of points of a certain infinite arithmetic progression. The results are applied to the investigation of controlled populational dynamics described by the Lottka–Volterra–Kolmogorov equations.
Received in September 2000
Bibliographic databases:
UDC: 517.977
Language: Russian
Citation: M. I. Zelikin, L. F. Zelikina, R. Hildebrand, “Asymptotics of Optimal Synthesis for One Class of Extremal Problems”, Differential equations. Certain mathematical problems of optimal control, Collected papers, Trudy Mat. Inst. Steklova, 233, Nauka, MAIK «Nauka/Inteperiodika», M., 2001, 95–124; Proc. Steklov Inst. Math., 233 (2001), 87–115
Citation in format AMSBIB
\Bibitem{ZelZelHil01}
\by M.~I.~Zelikin, L.~F.~Zelikina, R.~Hildebrand
\paper Asymptotics of Optimal Synthesis for One Class of Extremal Problems
\inbook Differential equations. Certain mathematical problems of optimal control
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2001
\vol 233
\pages 95--124
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm227}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1866980}
\zmath{https://zbmath.org/?q=an:1014.49028}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2001
\vol 233
\pages 87--115
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