Geodesic
A method for constructing an optimal control strategy in a linear terminal problem
Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2021), pp. 38-50.

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

This paper deals with an optimal control problem for a linear discrete system subject to unknown bounded disturbances, where the control goal is to steer the system with guarantees into a given terminal set while minimising the terminal cost function. We define an optimal control strategy which takes into account the state of the system at one future time instant and propose an efficient numerical method for its construction. The results of numerical experiments show an improvement in performance under the optimal control strategy in comparison to the optimal open-loop worst-case control while maintaining comparable computation times.
Keywords: linear system; disturbance; optimal control; control strategy; algorithm. 
@article{BGUMI_2021_2_a3,
     author = {D. A. Kastsiukevich and N. M. Dmitruk},
     title = {A method for constructing an optimal control strategy in a linear terminal problem},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {38--50},
     publisher = {mathdoc},
     volume = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2021_2_a3/}
}
TY  - JOUR
AU  - D. A. Kastsiukevich
AU  - N. M. Dmitruk
TI  - A method for constructing an optimal control strategy in a linear terminal problem
JO  - Journal of the Belarusian State University. Mathematics and Informatics
PY  - 2021
SP  - 38
EP  - 50
VL  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BGUMI_2021_2_a3/
LA  - en
ID  - BGUMI_2021_2_a3
ER  - 
%0 Journal Article
%A D. A. Kastsiukevich
%A N. M. Dmitruk
%T A method for constructing an optimal control strategy in a linear terminal problem
%J Journal of the Belarusian State University. Mathematics and Informatics
%D 2021
%P 38-50
%V 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BGUMI_2021_2_a3/
%G en
%F BGUMI_2021_2_a3
D. A. Kastsiukevich; N. M. Dmitruk. A method for constructing an optimal control strategy in a linear terminal problem. Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2021), pp. 38-50. http://geodesic.mathdoc.fr/item/BGUMI_2021_2_a3/

[1] H. Witsenhausen, “A minimax control problem for sampled linear systems”, IEEE Transactions on Automatic Control, 13(1) (1968), 5–21 | DOI | MR

[2] A. B. Kurzhanskii, “Upravlenie i nablyudenie v usloviyakh neopredelennosti”, Nauka, Moskva, 1977, 392 | Zbl

[3] N. N. Krasovskii, “Upravlenie dinamicheskoi sistemoi; Zadacha o minimume garantirovannogo rezultata”, Nauka, Moskva, 1985, 520 | MR | Zbl

[4] J. H. Lee, Y. u. Zhenghong, “Worst-case formulations of model predictive control for systems with bounded parameters”, Automatica, 33(5) (1997), 763–781 | DOI | MR | Zbl

[5] A. Bemporad, F. Borrelli, M. Morari, “Min-max control of constrained uncertain discrete-time linear systems”, IEEE Transactions on Automatic Control, 48(9) (2003), 1600–1606 | DOI | MR | Zbl

[6] N. V. Balashevich, R. Gabasov, F. M. Kirillova, “Postroenie optimalnykh obratnykh svyazei po matematicheskim modelyam s neopredelennostyu”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 44(2) (2004), 265–286 | MR | Zbl

[7] O. Kostyukova, E. Kostina, “Robust optimal feedback for terminal linear-quadratic control problems under disturbances”, Mathematical programming, 107(1–2) (2006), 131–153 | DOI | MR | Zbl

[8] N. M. Dmitruk, “Optimalnaya strategiya s odnim momentom zamykaniya v lineinoi zadache optimalnogo garantirovannogo upravleniya”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 58(5) (2018), 664–681 | DOI | Zbl

[9] S. Boyd, L. Vandenberghe, “Convex optimization”, Cambridge University Press, New York, 2004, 716 | MR

[10] T. Gal, “Postoptimal analyses, parametric programming and related topics: degeneracy, multicriteria decision making redundancy”, De Gruyter, Berlin, 199, 437