Geodesic
Existence of an~optimal control without convexity assumptions in a~first-order evolution system
Sbornik. Mathematics, Tome 192 (2001) no. 9, pp. 1381-1398

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An existence theorem is proved for an optimal control problem with constraints that is described by a first-order linear evolution equation, without the usual convexity assumptions relating to the control. The result is obtained by using properties of a multivalued integral and quasi-concavity conditions relating to the state variable. An example of a parabolic control system is treated at length. 
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     author = {A. A. Tolstonogov},
     title = {Existence of an~optimal control without convexity assumptions in a~first-order evolution system},
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     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_9_a5/}
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A. A. Tolstonogov. Existence of an~optimal control without convexity assumptions in a~first-order evolution system. Sbornik. Mathematics, Tome 192 (2001) no. 9, pp. 1381-1398. http://geodesic.mathdoc.fr/item/SM_2001_192_9_a5/