Geodesic
Non-anticipative strategies in guarantee optimization problems under functional constraints on disturbances
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 30 (2020) no. 4, pp. 553-571

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

For a dynamical system controlled under conditions of disturbances, a problem of optimizing the guaranteed result is considered. A feature of the problem is the presence of functional constraints on disturbances, under which, in general, the set of admissible disturbances is not closed with respect to the operation of “gluing up” of two of its elements. This circumstance does not allow to apply directly the methods developed within the differential games theory for studying the problem and, thus, leads to the necessity of modifying them appropriately. The paper provides a new notion of a non-anticipative control strategy. It is proved that the corresponding functional of the optimal guaranteed result satisfies the dynamic programming principle. As a consequence, so-called properties of $u$- and $v$-stability of this functional are established, which may allow, in the future, to obtain a constructive solution of the problem in the form of feedback (positional) controls.
Keywords: guarantee optimization, functional constraints, non-anticipative strategies, dynamic programming principle. 
@article{VUU_2020_30_4_a1,
     author = {M. I. Gomoyunov and D. A. Serkov},
     title = {Non-anticipative strategies in guarantee optimization problems under functional constraints on disturbances},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {553--571},
     publisher = {mathdoc},
     volume = {30},
     number = {4},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VUU_2020_30_4_a1/}
}
TY  - JOUR
AU  - M. I. Gomoyunov
AU  - D. A. Serkov
TI  - Non-anticipative strategies in guarantee optimization problems under functional constraints on disturbances
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2020
SP  - 553
EP  - 571
VL  - 30
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VUU_2020_30_4_a1/
LA  - en
ID  - VUU_2020_30_4_a1
ER  - 
%0 Journal Article
%A M. I. Gomoyunov
%A D. A. Serkov
%T Non-anticipative strategies in guarantee optimization problems under functional constraints on disturbances
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2020
%P 553-571
%V 30
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VUU_2020_30_4_a1/
%G en
%F VUU_2020_30_4_a1
M. I. Gomoyunov; D. A. Serkov. Non-anticipative strategies in guarantee optimization problems under functional constraints on disturbances. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 30 (2020) no. 4, pp. 553-571. http://geodesic.mathdoc.fr/item/VUU_2020_30_4_a1/