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 Mat. Sb. (N.S.), 1985, Volume 128(170), Number 1(9), Pages 35–49 (Mi msb2016)

On the lower alternating integral of Pontryagin in linear differential games of pursuit

M. S. Nikol'skii

Abstract: In this article the concept of the lower alternating integral of Pontryagin, which differs from the analogous concept of A. Azamov (Mat. Sb. (N.S.), 1982, v. 118(160), № 3, p. 422–430), is introduced. The properties of this object are studied in comparison with those of the alternating integral of Pontryagin. A procedure is given for application of the lower alternating integral of Pontryagin to linear differential games of pursuit, with special consideration for the question of using the lower alternating integral of Pontryagin when there are countably many measurements of the phase vector. The results are illustrated in two known differential games: “the boy and the crocodile” and the “control example of Pontryagin”.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Sbornik, 1987, 56:1, 33–47

Bibliographic databases:

UDC: 517.977
MSC: Primary 28B20, 90D25, 90D26; Secondary 52A20

Citation: M. S. Nikol'skii, “On the lower alternating integral of Pontryagin in linear differential games of pursuit”, Mat. Sb. (N.S.), 128(170):1(9) (1985), 35–49; Math. USSR-Sb., 56:1 (1987), 33–47

Citation in format AMSBIB
\Bibitem{Nik85} \by M.~S.~Nikol'skii \paper On the lower alternating integral of Pontryagin in linear differential games of pursuit \jour Mat. Sb. (N.S.) \yr 1985 \vol 128(170) \issue 1(9) \pages 35--49 \mathnet{http://mi.mathnet.ru/msb2016} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=805694} \zmath{https://zbmath.org/?q=an:0621.90109|0607.90099} \transl \jour Math. USSR-Sb. \yr 1987 \vol 56 \issue 1 \pages 33--47 \crossref{https://doi.org/10.1070/SM1987v056n01ABEH003022} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. A. B. Kurzhanskii, “Pontryagin's Alternated Integral in the Theory of Control Synthesis”, Proc. Steklov Inst. Math., 224 (1999), 212–225
2. A. B. Kurzhanskii, N. B. Melnikov, “On the problem of control synthesis: the Pontryagin alternating integral and the Hamilton–Jacobi equation”, Sb. Math., 191:6 (2000), 849–881
3. Daryin A., “Nonlinear synthesis for uncertain systems with diverse types of constraints”, Nonlinear Control Systems 2001, Ifac Symposia Series, 2002, 1511–1516
4. Dar'in, AN, “Control under indeterminacy and double constraints”, Differential Equations, 39:11 (2003), 1554
5. Iskanadjiev I., “Duality of the Alternating Integral for Quasi-Linear Differential Games”, Nonlinear Anal.-Model Control, 17:2 (2012), 169–181
6. A. Azamov, I. M. Iskanadjiev, “Pontryagin’s Alternating Integral for Differential Inclusions with Counteraction”, Contributions to Game Theory and Management, 5 (2012), 33–44
7. Iskanadjiev I.M., “On the Pontryagin Lower Alternating Integral”, J. Automat. Inf. Sci., 45:2 (2013), 33–40
8. Iskanadjiev I.M., “Lower Pontryagin'S Alternating Integral For Differential Inclusions”, Cybern. Syst. Anal., 51:5 (2015), 782–791
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