Abstract
We consider a control system described by the Goursat-Darboux equation. The system is controlled by distributed and boundary controls. The controls are subject to the constraints given as multivalued mappings with closed, possibly nonconvex, values depending on the phase variable. Alongside the initial constraints, we consider the convexified constraints and the constraints whose values are the extreme points of the convexified constraints. We study the questions of existence of solutions and establish connections between the solutions under various constraints.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 5, pp. 1116–1132, September–October, 2007.
Original Russian Text Copyright © 2007 Pogodaev N. I.
The author was supported by the Russian Foundation for Basic Research (Grant 06-01-00247-a).
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Pogodaev, N.I. On the properties of solutions to the Goursat-Darboux problem with boundary and distributed controls. Sib Math J 48, 897–912 (2007). https://doi.org/10.1007/s11202-007-0092-3
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DOI: https://doi.org/10.1007/s11202-007-0092-3