On the “bang-bang” principle for nonlinear evolution inclusions |
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Authors: | AA Tolstonogov DA Tolstonogov |
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Institution: | (1) Irkutsk Computer Center, Siberian Branch of Russian Academy of Science, P.O. Box 1233, RU-664033 Irkutsk, Russia, e-mail: aatol@icc.ru, RU;(2) Irkutsk Computer Center, Siberian Branch of Russian Academy of Science, P.O. Box 1233, RU-664033 Irkutsk, Russia, RU |
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Abstract: | We establish the existence of extreme solutions for a class of nonlinear evolution inclusions with non-convex right-hand
side defined on an evolution triple of Banach spaces. Then we show that extreme solutions which belong to the solution set
of the original system are in fact dense in the solutions of the system with convexified right-hand side. Subsequently we
use this density result to derive nonlinear and infinite-dimensional version of the “bang-bang” principle for control systems.
An example of a nonlinear parabolic distributed parameter system is also worked out in detail.
Received November 21, 1997 |
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