Differential Inclusions, Control and Optimization 20 (2000) 93-111
doi: 10.7151/dmdico.1007

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Marcus Wagner

Cottbus University of Technology, Institute of Mathematics
Karl-Marx-Str. 17, P.O. Box 10 13 44, D-03013 Cottbus, Germany

e-mail: wagner@math.tu-cottbus.de


For a multidimensional control problem (P)K involving controls u ∈ L, we construct a dual problem (D)K in which the variables ν to be paired with u are taken from the measure space rca (Ω,B) instead of (L)*. For this purpose, we add to (P)K a Baire class restriction for the representatives of the controls u. As main results, we prove a strong duality theorem and saddle-point conditions.

Keywords: multidimensional control problems, strong duality, saddle-point conditions, Baire classification.

1991 Mathematics Subject Classification: Primary: 49N15; Secondary: 26A21, 26E25, 28A20, 49K20, 90B06.


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Received 19 November 1999
Revised 1 March 2000