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On Pontryagin's First Direct Method in Pursuit Problems
A. A. Azamov Institute for Mathematics and Information Technologies of the National Academy of Sciences of Uzbekistan
Abstract:
We describe an example of a three-dimensional linear differential game with convex compact sets of control. In this example, the integrand in Pontryagin's first direct method is discontinuous on a set of positive measure.
Keywords:
linear differential game, Pontryagin direct method, convex compact set of control, stroboscopic strategy, Lebesgue measurability, Borel measurability, Aumann integral, Hausdorff metric, Cantor discontinuum
DOI:
https://doi.org/10.4213/mzm6603
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English version:
Mathematical Notes, 2011, 90:2, 157–161
Bibliographic databases:
UDC:
519.978.2 Received: 06.10.2008
Citation:
A. A. Azamov, “On Pontryagin's First Direct Method in Pursuit Problems”, Mat. Zametki, 90:2 (2011), 163–167; Math. Notes, 90:2 (2011), 157–161
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/mz6603https://doi.org/10.4213/mzm6603 http://mi.mathnet.ru/eng/mz/v90/i2/p163
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