The problem of package guidance under incomplete information and integral signal of observation
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 373-388.

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

The problem of guaranteed closed-loop guidance at a given time is studied for a dynamical control system. The initial state is unknown, but belongs to a given finite set of admissible initial states. The information on the position of the system is represented as an integral signal. The control system of ordinary differential equations is reduced to a system of functional-differential equations with the simplification of the form of the signal. The problem of package guidance is formulated for such system and a solvability criterion is proved. For a particular case of the integral signal, the solvability criterion is rewritten in a simplified form. An example is given illustrated the proposed technique by a specific linear control system of differential equations.
Keywords: control, incomplete information, linear systems.
@article{SEMR_2018_15_a88,
     author = {P. G. Surkov},
     title = {The problem of package guidance under incomplete information and integral signal of observation},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {373--388},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a88/}
}
TY  - JOUR
AU  - P. G. Surkov
TI  - The problem of package guidance under incomplete information and integral signal of observation
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2018
SP  - 373
EP  - 388
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a88/
LA  - ru
ID  - SEMR_2018_15_a88
ER  - 
%0 Journal Article
%A P. G. Surkov
%T The problem of package guidance under incomplete information and integral signal of observation
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2018
%P 373-388
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a88/
%G ru
%F SEMR_2018_15_a88
P. G. Surkov. The problem of package guidance under incomplete information and integral signal of observation. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 373-388. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a88/

[1] Yu. S. Osipov, “Control Packages: an Approach to Solution of Positional Control Problems with Incomplete Information”, Russian Mathematical Surveys, 61:4 (2006), 611–661 | DOI | MR | Zbl

[2] A. V. Kryazhimskii, Yu. S. Osipov, “Idealizirovannye pakety programm i zadachi pozitsionnogo upravleniya s nepolnoy informatsiey (Idealized program packages and positional control problems with incomplete information)”, Trudy Inst. Matem. Mekhan. Uro RAN, 15, no. 3, 2009, 139–157

[3] A. V. Kryazhimskiy, Yu. S. Osipov, “On the Solvability of Problems of Guaranteeing Control for Partially Observable Linear Dynamical Systems”, Proceedings of the Steklov Institute of Mathematics, 277 (2012), 144–159 | DOI | MR | Zbl

[4] N. N. Krasovskii, Game Problems with Oncoming Motions, Nauka, M., 1970 | MR | Zbl

[5] A. I. Subbotin, A. G. Chentsov, Guarantee Optimization in Control Problems, Nauka, M., 1981 | MR | Zbl

[6] A. V. Kryazhimskiy, N. V. Strelkovskii, “An Open-Loop Criterion for the Solvability of a Closed-Loop Guidance Problem with Incomplete Information. Linear Control Systems”, Proceedings of the Steklov Institute of Mathematics, 291:1 (2015), 113–127 | DOI | MR | Zbl

[7] V. I. Maksimov, “Guidance Problem for a Distributed Sytem with Incomplete Information on the State Coordinates and an Unknown Initial State”, Differential Equations, 52:11 (2016), 1442–1452 | DOI | MR | Zbl

[8] V. I. Maksimov, “Differential Guidance Game with Incomplete Information on the State Coordinates and Unknown Initial State”, Differential Equations, 51:12 (2015), 1656–1665 | DOI | MR | Zbl

[9] V. L. Rozenberg, “A Control Problem under Incomplete Information for a Linear Stochastic Differential Equation”, Proceedings of the Steklov Institute of Mathematics, 295:1 (2016), 145–155 | DOI | MR | Zbl

[10] P. G. Surkov, “The Problem of Package Guidance with Incomplete Information for a Linear Control System with a Delay”, Computational Mathematics and Modeling, 28:4 (2017), 504–516 | DOI | MR | Zbl

[11] M. S. Blizorukova, “On a control problem for a linear system with delay in the control”, Proceedings of the Steklov Institute of Mathematics, 297:1 (2017), 35–42 | DOI | MR | Zbl

[12] N. L. Grigorenko, A. E. Rumyantsev, “Terminal control of a nonlinear process under disturbances”, Proceedings of the Steklov Institute of Mathematics, 297 (2017), 108–116 | DOI | MR | Zbl

[13] S. Nakagiri, “On the Fundamental Solution of Delay-Differential Equations in Banach Spaces”, J. Differential Equations, 41:2 (1981), 349–368 | DOI | MR | Zbl

[14] N. V. Azbelev, V. P. Maksimov, L. F. Rakhmatullina, Introduction to The Theory of Functional Differential Equations: Methods and Applications, Hindawi Publishing Corporation, Cairo, 2007 | MR

[15] Yu. F. Dolgii, P. G. Surkov, Mathematical models of dynamical systems with delay: tutorial, Publishing house of Ural University, Ekaterinburg, 2012

[16] J. K. Hale, S. M. Verduyn Lunel, Introduction to Functional-Differential Equations, Applied Mathematical Sciences, 99, Springer-Verlag, New York, 1993 | DOI | MR

[17] L. S. Pontryagin, Ordinary differential equations, Nauka, M., 1982 | MR

[18] F. R. Gantmacher, The Theory of Matrices, Chelsea Publishing Company, New York, 1959 | MR