Geodesic
A parallel algorithm for constructing approximate attainable sets of nonlinear control systems
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 4, pp. 459-472 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper investigates the effectiveness of shared memory parallel programming approach for constructing approximate attainable sets of nonlinear control systems in a finite-dimensional Euclidean space. In this study, we propose a parallel iterative algorithm for constructing approximate attainable sets employing a regular Cartesian grid for spatial discretization. The proposed algorithm has been designed for implementation on SMP systems and handles such issues as data decomposition, threads synchronization and distribution of work between multiple threads. Numerical experiments on a system with two quad-core processors confirmed a high efficiency of shared memory parallel programming approach for applying grid-based methods to construct approximate attainable sets.
Keywords: attainability set, parallel algorithm, control system, grid-based method. 
@article{VUU_2015_25_4_a2,
     author = {A. A. Zimovets and A. R. Matviichuk},
     title = {A parallel algorithm for constructing approximate attainable sets of nonlinear control systems},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {459--472},
     year = {2015},
     volume = {25},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2015_25_4_a2/}
}
TY  - JOUR
AU  - A. A. Zimovets
AU  - A. R. Matviichuk
TI  - A parallel algorithm for constructing approximate attainable sets of nonlinear control systems
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2015
SP  - 459
EP  - 472
VL  - 25
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VUU_2015_25_4_a2/
LA  - ru
ID  - VUU_2015_25_4_a2
ER  - 
%0 Journal Article
%A A. A. Zimovets
%A A. R. Matviichuk
%T A parallel algorithm for constructing approximate attainable sets of nonlinear control systems
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2015
%P 459-472
%V 25
%N 4
%U http://geodesic.mathdoc.fr/item/VUU_2015_25_4_a2/
%G ru
%F VUU_2015_25_4_a2
A. A. Zimovets; A. R. Matviichuk. A parallel algorithm for constructing approximate attainable sets of nonlinear control systems. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 4, pp. 459-472. http://geodesic.mathdoc.fr/item/VUU_2015_25_4_a2/

[1] Krasovskii N. N., Theory of motion control, Nauka, Moscow, 1968, 476 pp. | MR

[2] Nikol'skii M. S., “A method of approximating an attainable set for a differential inclusion”, USSR Computational Mathematics and Mathematical Physics, 28:4 (1988), 192–194 | DOI | MR | Zbl

[3] Komarov V. A., Pevchikh K. E., “A method of approximating attainability sets for differential inclusions with a specified accuracy”, USSR Computational Mathematics and Mathematical Physics, 31:1 (1991), 109–112 | MR | Zbl

[4] Guseinov Kh. G., Moiseyev A. N., Ushakov V. N., “The approximation of reachable domains of control systems”, Journal of Applied Mathematics and Mechanics, 62:2 (1998), 169–175 | DOI | MR

[5] Ushakov V. N., Matviichuk A. R., Ushakov A. V., “Approximations of attainability sets and of integral funnels of differential inclusions”, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2011, no. 4, 23–39 (in Russian) | Zbl

[6] Pakhotinskikh V. Yu., Constructing solutions for control problems on a finite time interval, Cand. Sci. (Phys.-Math.) Dissertation, Chelyabinsk, 2005, 160 pp. (in Russian)

[7] Zimovets A. A., “A boundary layer method for the construction of approximate attainability sets of control systems”, Vestn. Yuzhno-Ural. Gos. Univ. Ser. Mat. Mekh. Fiz., 5:1 (2013), 18–25 (in Russian)