Relaxation in the optimal control problem for the Goursat–Darboux system

N. I. Pogodaev

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

Abstract: We consider the optimal control problem for a system described by the Goursat–Darboux equation. The system is controlled by distributed and boundary controls satisfying mixed nonconvex constraints. For this problem we prove an analog of the classical Bogolyubov relaxation theorem.

Keywords: continuous selector, boundary and distributed controls, relaxation, expansion.

UDC: 517.977

Received: 03.02.2010

 English version: Siberian Mathematical Journal, 2011, 52:1, 78–90

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