Geodesic
The asymptotics of the optimal value of the performance functional in a linear optimal control problem in the regular case
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 55-65 
A. R. Danilin; Yu. V. Parysheva. The asymptotics of the optimal value of the performance functional in a linear optimal control problem in the regular case. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 55-65. http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a4/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

An optimal control problem is investigated for a linear system with fast and slow variables, a convex terminal performance functional depending on the slow variables, and smooth geometric constraints on the control. Sufficient regularity conditions are presented for the asymptotics of a solution of this problem, and a complete asymptotic expansion of the optimal value of the performance functional in powers of a small parameter is constructed.

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