Geodesic
$l$-Problem of moments in problems of optimal control and state estimation for multidimensional fractional linear systems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 2, Tome 231 (2024), pp. 107-114

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In this paper, we consider multidimensional dynamical systems whose states are described by systems of linear fractional differential equations of different order. We examine problems of optimal control and optimal state estimation for systems with the Caputo and Riemann–Liouville fractional differentiation operators. We prove that under certain conditions both problems can be reduced to the $l$-problem of moments. For the resulting problem, the solvability conditions are verified and, in a number of cases, exact solutions are constructed.
Keywords: optimal control, dynamical system, fractional dynamics, fractional derivative, $l$-problem of moments
Mots-clés : optimal estimation 
@article{INTO_2024_231_a10,
     author = {S. S. Postnov},
     title = {$l${-Problem} of moments in problems of optimal control and state estimation for multidimensional fractional linear systems},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {107--114},
     publisher = {mathdoc},
     volume = {231},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2024_231_a10/}
}
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S. S. Postnov. $l$-Problem of moments in problems of optimal control and state estimation for multidimensional fractional linear systems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 2, Tome 231 (2024), pp. 107-114. http://geodesic.mathdoc.fr/item/INTO_2024_231_a10/