Geodesic
Optimal behavior control of an initial-boundary problem solution modelling rotation of a solid body with the flexible rod
Modelirovanie i analiz informacionnyh sistem, Tome 21 (2014) no. 5, pp. 78-92.

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

An initial-boundary problem modelling the rotation of discrete-continuum mechanical system, which consists from a solid and the rigidly connected flexible rod. To solve the problem we determine a solution notion, prove its existence, uniqueness, and continuous dependence from start conditions and parameters of the boundary task. Are resolved tasks of solution rotation from the start phase state to the finish one at a specified time moment and with the controller function norm minimum in the $L_\infty (0,T)$ space and time control problem with a limited norm of controller function in the specified space. Maximum principe was formulated, and an algorithm of optimal control modelling is proposed. The moments problem is used as an investigation method
Keywords: initial-boundary task, discrete-continuum mechanical system, optimal control, time control problem. 
@article{MAIS_2014_21_5_a4,
     author = {E. P. Kubishkin and M. S. Triakhov},
     title = {Optimal behavior control of an initial-boundary problem solution modelling rotation of a solid body with the flexible rod},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {78--92},
     publisher = {mathdoc},
     volume = {21},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2014_21_5_a4/}
}
TY  - JOUR
AU  - E. P. Kubishkin
AU  - M. S. Triakhov
TI  - Optimal behavior control of an initial-boundary problem solution modelling rotation of a solid body with the flexible rod
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2014
SP  - 78
EP  - 92
VL  - 21
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2014_21_5_a4/
LA  - ru
ID  - MAIS_2014_21_5_a4
ER  - 
%0 Journal Article
%A E. P. Kubishkin
%A M. S. Triakhov
%T Optimal behavior control of an initial-boundary problem solution modelling rotation of a solid body with the flexible rod
%J Modelirovanie i analiz informacionnyh sistem
%D 2014
%P 78-92
%V 21
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2014_21_5_a4/
%G ru
%F MAIS_2014_21_5_a4
E. P. Kubishkin; M. S. Triakhov. Optimal behavior control of an initial-boundary problem solution modelling rotation of a solid body with the flexible rod. Modelirovanie i analiz informacionnyh sistem, Tome 21 (2014) no. 5, pp. 78-92. http://geodesic.mathdoc.fr/item/MAIS_2014_21_5_a4/

[1] Beryuk V. E., Dinamika i optimizatsiya robototekhnicheskikh sistem, Naukova Dumka, Kiev, 1989

[2] Ye. P. Kubyshkin, “Optimal control of the rotation of a solid with a flexible rod”, Journal of Applied Mathematics and Mechanics, 56:2 (1992), 205–214

[3] W. Krabs, N. Chi-Long, “On the Controllability of a Robot Arm”, Mathematical Methods in the Applied Sciences, 21 (1998), 25–42

[4] N. I. Akhiezer, I. M. Glazman, Theory of linear operators in Hilbert space, 2 ed., Dover, 1993, 377 pp.

[5] Vibratsii v tekhnike: Spravochnik, M., 1978, 362 pp.

[6] M. G. Krein, A. A. Nudelman, The Markov moment problem and extremal problems. Ideas and problems of P. L. Chebyshev and A. A. Markov and their further development, Translations of Mathematical Monographs, v. 50, American Mathematical Society, Providence, R.I., 1977, 417 pp.

[7] B. Z. Vulikh, Introduction to Functional Analysis for Scientists and Technologists, Elsevier Science and Technology, 1963, 404 pp.