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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Volume 304, Pages 221–234
DOI: https://doi.org/10.4213/tm3968 (Mi tm3968) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Stable Functionals of Neutral-Type Dynamical Systems

N. Yu. Lukoyanovab, A. R. Plaksinab

a N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990 Russia
b Ural Federal University named after the First President of Russia B. N. Yeltsin, ul. Mira 19, Yekaterinburg, 620002 Russia
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DOI: https://doi.org/10.4213/tm3968
Abstract: We consider a controlled dynamical system under noisy conditions. Its motion is described by functional differential equations of neutral type in the form of J. Hale. A functional of the motion history is said to be stable with respect to this system if there exists a control strategy that guarantees the monotonicity of this functional for any noise. We study various nonlocal and infinitesimal conditions for the stability of functionals.
Keywords: differential games optimal control, coinvariant derivatives, directional derivatives, Hamilton–Jacobi equations, stable functionals.
Received: August 2, 2018
Revised: September 20, 2018
Accepted: January 10, 2019
English version:
Proceedings of the Steklov Institute of Mathematics, 2019, Volume 304, Pages 205–218
DOI: https://doi.org/10.1134/S0081543819010140
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: N. Yu. Lukoyanov, A. R. Plaksin, “Stable Functionals of Neutral-Type Dynamical Systems”, Optimal control and differential equations, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 304, Steklov Math. Inst. RAS, Moscow, 2019, 221–234; Proc. Steklov Inst. Math., 304 (2019), 205–218
Citation in format AMSBIB
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\by N.~Yu.~Lukoyanov, A.~R.~Plaksin
\paper Stable Functionals of Neutral-Type Dynamical Systems
\inbook Optimal control and differential equations
\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
\yr 2019
\vol 304
\pages 221--234
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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