Geodesic
Bogolyubov's theorem under constraints generated by a~controlled second-order evolution system
Izvestiya. Mathematics , Tome 67 (2003) no. 5, pp. 1031-1060

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove an analogue of Bogolyubov's theorem with constraints in the form of a controlled second-order evolution system. The main assertion of this theorem deals with relations between the values of an integral functional that is non-convex with respect to control on the solutions of a controlled system with non-convex constraints on the control and the values of the functional convexified with respect to control on the solutions of a controlled system with convexified constraints. This theorem also establishes relations between the solutions of non-convex and convexified controlled systems. We apply the theorem to the problem of minimizing a non-convex integral functional on the solutions of a non-convex controlled system. We consider in detail an example of a non-linear hyperbolic system. 
@article{IM2_2003_67_5_a7,
     author = {A. A. Tolstonogov},
     title = {Bogolyubov's theorem under constraints generated by a~controlled second-order evolution system},
     journal = {Izvestiya. Mathematics },
     pages = {1031--1060},
     publisher = {mathdoc},
     volume = {67},
     number = {5},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2003_67_5_a7/}
}
TY  - JOUR
AU  - A. A. Tolstonogov
TI  - Bogolyubov's theorem under constraints generated by a~controlled second-order evolution system
JO  - Izvestiya. Mathematics 
PY  - 2003
SP  - 1031
EP  - 1060
VL  - 67
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2003_67_5_a7/
LA  - en
ID  - IM2_2003_67_5_a7
ER  - 
%0 Journal Article
%A A. A. Tolstonogov
%T Bogolyubov's theorem under constraints generated by a~controlled second-order evolution system
%J Izvestiya. Mathematics 
%D 2003
%P 1031-1060
%V 67
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2003_67_5_a7/
%G en
%F IM2_2003_67_5_a7
A. A. Tolstonogov. Bogolyubov's theorem under constraints generated by a~controlled second-order evolution system. Izvestiya. Mathematics , Tome 67 (2003) no. 5, pp. 1031-1060. http://geodesic.mathdoc.fr/item/IM2_2003_67_5_a7/