Geodesic
Real-time calculation of current optimal feedbacks for a delay system
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 10, pp. 1744-1757 
R. Gabasov; F. M. Kirillova; O. P. Yarmosh. Real-time calculation of current optimal feedbacks for a delay system. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 10, pp. 1744-1757. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a3/
@article{ZVMMF_2006_46_10_a3,
     author = {R. Gabasov and F. M. Kirillova and O. P. Yarmosh},
     title = {Real-time calculation of current optimal feedbacks for a~delay system},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1744--1757},
     year = {2006},
     volume = {46},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a3/}
}
TY  - JOUR
AU  - R. Gabasov
AU  - F. M. Kirillova
AU  - O. P. Yarmosh
TI  - Real-time calculation of current optimal feedbacks for a delay system
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2006
SP  - 1744
EP  - 1757
VL  - 46
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a3/
LA  - ru
ID  - ZVMMF_2006_46_10_a3
ER  - 
%0 Journal Article
%A R. Gabasov
%A F. M. Kirillova
%A O. P. Yarmosh
%T Real-time calculation of current optimal feedbacks for a delay system
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2006
%P 1744-1757
%V 46
%N 10
%U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a3/
%G ru
%F ZVMMF_2006_46_10_a3

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

A linear optimal control problem for a nonstationary system with a single delay state variable is examined. A fast implementation of the dual method is proposed in which a key role is played by a quasi-reduction of the fundamental matrices of solutions to the homogeneous part of the delay models under analysis. As a result, an iteration step of the dual method involves only the integration of auxiliary systems of ordinary differential equations over short time intervals. A real-time algorithm is described for calculating optimal feedback controls. The results are illustrated by the optimal control problem for a second-order stationary system with a fixed delay.

[1] Pontryagin L. S., Boltyanskii V. T., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1976 | Zbl

[2] Fedorenko R. P., Priblizhennye metody resheniya zadach optimalnogo upravleniya, Nauka, M., 1978 | Zbl

[3] Bellman R., Dreifus S., Prikladnye zadachi dinamicheskogo programmirovaniya, Nauka, M., 1965 | Zbl

[4] Kim A. B., Rublev S. S., Chei E. S., “K zadache analiticheskogo konstruirovaniya regulyatorov dlya sistem s posledeistviem”, Tr. In-ta matem. i mekhan. UrO RAN. Ekaterinburg, 11, no. 1, 2005, 11–121

[5] Gabasov R., Kirillova F. M., “Printsipy optimalnogo upravleniya”, Dokl. HAH Belarusi, 48:1 (2004), 15–18 | MR

[6] Gabasov R., Kirillova F. M., Kostyukova O. I., “Postroenie optimalnykh upravlenii tipa obratnoi svyazi v lineinoi zadache”, Dokl. AN SSSR, 320:6 (1991), 1294–1299 | MR

[7] Gabasov R., Kirillova F. M., Balashevich N. V., “On the synthesis problem for optimal conrol systems”, SIAM J. Control Optim., 39:4 (2000), 1008–1042 | DOI | MR | Zbl

[8] Gabasov R., Kirillova F. M., Balashevich N. V., “Open-loop and closed-loop optimization of linear control systems”, Asian J. Control, 2:3 (2000), 155–168 | MR

[9] Balashevich H. V., Gabasov R., Kirillova F. M., “Chislennye metody programmnoi i pozitsionnoi optimizatsii lineinykh sistem upravleniya”, Zh. vychisl. matem. i matem. fiz., 40:6 (2000), 838–859 | MR | Zbl

[10] Manitius A., “Feedback controllers for a wind tunnel model involving a delay: Analytical design and numerical simulation”, IEEE Trans. Automat. Control, 29:12 (1984), 1058–1068 | DOI | MR

[11] Manitius A., Tran H., “Numerical simulation of a nonlinear feedback controller for a wide tunnel model involving a time delay”, Optimal Control Applic. and Meth., 7 (1986), 19–39 | DOI | Zbl

[12] Kim A., Pimenov V. et al., Time-delay systems. Toolbox. Beta version, Inst. Math. and Mech. Ural Branch of RAS, Ekaterinburg. Eng. Res. Center for Advanced Control and Instrument, Korea, 1999

[13] Gabasov R., Adaptive method for solving linear programming problems, Preprint Series, Inst. Statistic and Math. Univ., Karlsruhe, 1994

[14] Gabasov P., Kirillova F. M., Tyatyushkin A. I., Konstruktivnye metody optimizatsii. Ch. I. Lineinye zadachi, Universitetskoe, Minsk, 1984 | MR