Geodesic
Measurement process control in dynamical systems
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2013), pp. 105-109 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The problem of observation process optimization of dynamical system motion under random perturbations is considered. Moreover, all types of uncertainty (both external perturbations and measurement error) are treated as random variables with given statistical characteristics. The transition function of the considered dynamic process contains a vector of unknown parameters. Using Bayesian method the original problem is reduced to the solution of a determinate optimal control problem. The paper demonstrates the possibility of using Bellman's principle of dynamic programming to the quick action problem with a nonlinear system. Under constrains on control examined the necessary and sufficient conditions of optimal control are found. The obtained results are illustrated on an example. Bibliogr. 4.
Keywords: random variable, nonsmooth analysis, dynamic programming, strict extremum, necessary and sufficient conditions. 
@article{VSPUI_2013_4_a12,
     author = {V. V. Karelin and A. V. Fominyh},
     title = {Measurement process control in dynamical systems},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {105--109},
     year = {2013},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2013_4_a12/}
}
TY  - JOUR
AU  - V. V. Karelin
AU  - A. V. Fominyh
TI  - Measurement process control in dynamical systems
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2013
SP  - 105
EP  - 109
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2013_4_a12/
LA  - ru
ID  - VSPUI_2013_4_a12
ER  - 
%0 Journal Article
%A V. V. Karelin
%A A. V. Fominyh
%T Measurement process control in dynamical systems
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2013
%P 105-109
%N 4
%U http://geodesic.mathdoc.fr/item/VSPUI_2013_4_a12/
%G ru
%F VSPUI_2013_4_a12
V. V. Karelin; A. V. Fominyh. Measurement process control in dynamical systems. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2013), pp. 105-109. http://geodesic.mathdoc.fr/item/VSPUI_2013_4_a12/

[1] Dynkin E. B., Jushkevich A. A., Markov decision processes and their applications, Nauka, M., 1975, 338 pp. | MR

[2] Karelin V. V., “Adaptive optimal strategies in controlled Markov processes”, Advances in Optimization Proceedings of 6th French-German Colloquium of Optimization (FRG, 1991), 518–525 | MR

[3] Chernous'ko F. A., Kolmanovskij V. B., Optimal control for random disturbances, Nauka, M., 1978, 352 pp. | MR

[4] Bellman R., Dynamic Programming, Per. s angl. I. M. Andreeva i dr., ed. N. N. Vorobiev, Izd-vo inostr. lit., M., 1960, 400 pp. | MR