Geodesic
Necessary optimality conditions of the second oder in~a~stochastic optimal control problem with delay argument
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 4, pp. 620-635

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

The optimal control problem of nonlinear stochastic systems which mathematical model is given by Ito stochastic differential equation with delay argument is considered. Assuming that the concerned region is open for the control by the first and the second variation (classical sense) of the quality functional we obtain the necessary optimality condition of the first and the second order. In the particular case we receive the stochastic analog of the Legendre—Clebsch condition and some constructively verified conclusions from the second order necessary condition. We investigate theLegendre–Clebsch conditions for the degeneration case and obtain the necessary conditions of optimality for a special control, in the classical sense.
Keywords: stochastic control problem, admissible control, optimal control, first and second order variation of quality functional, a necessary condition for the stochastic analogue of the Euler equations, stochastic analog of the Legendre–Clebsch, singular control the classic sense. 
@article{VSGTU_2016_20_4_a3,
     author = {R. O. Mastaliev},
     title = {Necessary optimality conditions of the second oder in~a~stochastic optimal control problem with delay argument},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {620--635},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2016_20_4_a3/}
}
TY  - JOUR
AU  - R. O. Mastaliev
TI  - Necessary optimality conditions of the second oder in~a~stochastic optimal control problem with delay argument
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2016
SP  - 620
EP  - 635
VL  - 20
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2016_20_4_a3/
LA  - ru
ID  - VSGTU_2016_20_4_a3
ER  - 
%0 Journal Article
%A R. O. Mastaliev
%T Necessary optimality conditions of the second oder in~a~stochastic optimal control problem with delay argument
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2016
%P 620-635
%V 20
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2016_20_4_a3/
%G ru
%F VSGTU_2016_20_4_a3
R. O. Mastaliev. Necessary optimality conditions of the second oder in~a~stochastic optimal control problem with delay argument. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 4, pp. 620-635. http://geodesic.mathdoc.fr/item/VSGTU_2016_20_4_a3/