On solutions of an~evolution control system depending on parameters
Sbornik. Mathematics, Tome 194 (2003) no. 9, pp. 1383-1409
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A control system governed by a non-linear first-order
evolution equation with mixed non-convex control constraints
is examined. The system depends on parameters entering all
its data, including the non-linear evolution operator and
the control constraints. The system with convexified control
constraints is also considered. The general concept of $G$-convergence of operators is used for the proof of the existence of selectors continuously dependent on the parameters with
values in the solution set of the original system; a continuous version of the selector relaxation theorem is also proved, which concerns the approximation of the continuous solution selectors with convexified constraints by continuous solution selectors
of the original system. An example of a parabolic control system
is discussed.
@article{SM_2003_194_9_a4,
author = {A. A. Tolstonogov},
title = {On solutions of an~evolution control system depending on parameters},
journal = {Sbornik. Mathematics},
pages = {1383--1409},
publisher = {mathdoc},
volume = {194},
number = {9},
year = {2003},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2003_194_9_a4/}
}
A. A. Tolstonogov. On solutions of an~evolution control system depending on parameters. Sbornik. Mathematics, Tome 194 (2003) no. 9, pp. 1383-1409. http://geodesic.mathdoc.fr/item/SM_2003_194_9_a4/