This article is cited in 3 papers

On the properties of solutions to the Goursat–Darboux problem with boundary and distributed controls

N. I. Pogodaev

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

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.

Keywords: continuous selectors, boundary and distributed control, density, boundary property, necessary and sufficient conditions for closure.

UDC: 517.955

Received: 26.04.2006

 English version: Siberian Mathematical Journal, 2007, 48:5, 897–912

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