Geodesic
Features of the phase dynamics of fractional two-dimensional linear control systems for various differentiation operator
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 217 (2022), pp. 81-96

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

This paper is devoted to the study of the phase dynamics of fractional linear systems with control. Two-dimensional systems with concentrated parameters are considered in most detail in the cases where the fractional differentiation operators in the governing equations are understood in the Caputo–Fabrizio sense. Systems modeled by equations with Atangana–Baleano and Prabhakara operators are also considered. We obtain and examine analytic solutions and boundary trajectories of systems, which determine domains of admissible values of the phase coordinates. The statement of the moment $l$-problem for the systems considered and its solvability are analyzed. An example of solving this problem in the case where the control is an essentially bounded function on a interval is given.
Keywords: fractional dynamical system, optimal control, fractional derivative, $l$-problem of moments. 
@article{INTO_2022_217_a9,
     author = {S. S. Postnov},
     title = {Features of the phase dynamics of fractional two-dimensional linear control systems for various differentiation operator},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {81--96},
     publisher = {mathdoc},
     volume = {217},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_217_a9/}
}
TY  - JOUR
AU  - S. S. Postnov
TI  - Features of the phase dynamics of fractional two-dimensional linear control systems for various differentiation operator
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2022
SP  - 81
EP  - 96
VL  - 217
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2022_217_a9/
LA  - ru
ID  - INTO_2022_217_a9
ER  - 
%0 Journal Article
%A S. S. Postnov
%T Features of the phase dynamics of fractional two-dimensional linear control systems for various differentiation operator
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2022
%P 81-96
%V 217
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2022_217_a9/
%G ru
%F INTO_2022_217_a9
S. S. Postnov. Features of the phase dynamics of fractional two-dimensional linear control systems for various differentiation operator. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 217 (2022), pp. 81-96. http://geodesic.mathdoc.fr/item/INTO_2022_217_a9/