Geodesic
Well-posed extensions of unstable control problems with integral constraints
Izvestiya. Mathematics , Tome 63 (1999) no. 3, pp. 599-630

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The paper deals with the reconstruction of the natural asymptotic behaviour of sets of admissible elements and their information images (“attainable” elements) by relaxing integral constraints. This asymptotic behaviour can be “lost” in the orthodox data processing. Procedures are suggested that can be applied, in particular, to the study of the asymptotic behaviour of the attainability domains of control systems under a vanishingly small problem relaxation. 
@article{IM2_1999_63_3_a7,
     author = {A. G. Chentsov},
     title = {Well-posed extensions of unstable control problems with integral constraints},
     journal = {Izvestiya. Mathematics },
     pages = {599--630},
     publisher = {mathdoc},
     volume = {63},
     number = {3},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1999_63_3_a7/}
}
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A. G. Chentsov. Well-posed extensions of unstable control problems with integral constraints. Izvestiya. Mathematics , Tome 63 (1999) no. 3, pp. 599-630. http://geodesic.mathdoc.fr/item/IM2_1999_63_3_a7/