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Teoriya Veroyatnostei i ee Primeneniya, 2022, Volume 67, Issue 4, Pages 672–687
DOI: https://doi.org/10.4213/tvp5476 (Mi tvp5476) 		 
On optimal linear regulator with polynomial process of external excitations

E. S. Palamarchukab

a Central Economics and Mathematics Institute of the Russian Academy of Sciences, Moscow, Russia
b National Research University "Higher School of Economics", Moscow
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DOI: https://doi.org/10.4213/tvp5476
Abstract: A linear control system over an infinite time-horizon is considered, where external excitations are defined as polynomials based on a time-varying Ornstein–Uhlenbeck process. An optimal control law with respect to long-run average type criteria is established. It is shown that the optimal control has the form of a linear feedback law, where the affine term satisfies a backward linear stochastic differential equation. The normalizing functions in the optimality criteria depend on the stability rate of the dynamic equation for the Ornstein–Uhlenbeck process.
Keywords: linear regulator, polynomial process, Ornstein–Uhlenbeck process, pathwise optimality.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation AAAA-A21-121012090157-9
This research was carried out in the framework of the Research Project “Developing the theory and software and mathematical tools for the investigation of socio-economic processes” AAAA-A21-121012090157-9.
Received: 16.01.2021
Revised: 16.04.2022
Accepted: 17.06.2022
English version:
Theory of Probability and its Applications, 2022, Volume 67, Issue 4, Pages 535–547
DOI: https://doi.org/10.1137/S0040585X97T991131
Bibliographic databases:
Document Type: Article
PACS: 02.30.Yy 02.50.Fz 05.40.-a
MSC: 60H30 49N10 60G15
Language: Russian
Citation: E. S. Palamarchuk, “On optimal linear regulator with polynomial process of external excitations”, Teor. Veroyatnost. i Primenen., 67:4 (2022), 672–687; Theory Probab. Appl., 67:4 (2022), 535–547
Citation in format AMSBIB
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\by E.~S.~Palamarchuk
\paper On optimal linear regulator with polynomial process of external excitations
\jour Teor. Veroyatnost. i Primenen.
\yr 2022
\vol 67
\issue 4
\pages 672--687
\mathnet{http://mi.mathnet.ru/tvp5476}
\crossref{https://doi.org/10.4213/tvp5476}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4466411}
\transl
\jour Theory Probab. Appl.
\yr 2022
\vol 67
\issue 4
\pages 535--547
\crossref{https://doi.org/10.1137/S0040585X97T991131}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85153189026}
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