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Teoriya Veroyatnostei i ee Primeneniya, 2023, Volume 68, Issue 1, Pages 38–56
DOI: https://doi.org/10.4213/tvp5567 (Mi tvp5567) 		 
Optimal linear-quadratic regulator for a stochastic system under mutually inverse time preferences in the cost

E. S. Palamarchukab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b National Research University "Higher School of Economics", Moscow
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DOI: https://doi.org/10.4213/tvp5567
Abstract: We investigate a long-run behavior of a linear stochastic system. It is assumed that the quadratic cost includes a time-varying function and its multiplicative inverse. Such a specification reflects the fact that time preferences used by agents to assess different types of losses evolve in opposite directions. We consider the case when priority is set for the losses associated with state deviations. The optimal control law is derived with respect to extended long-run average cost criteria. We provide conditions for the existence of an alternative control strategy, which is also optimal and is based on a solution of an algebraic Riccati equation.
Keywords: linear regulator of a stochastic system, time preferences, long-run average.
Funding agency Grant number
Russian Science Foundation 18-71-10097
This research was supported by the Russian Science Foundation under grant no. 18-71-10097, https://rscf.ru/project/18-71-10097.
Received: 02.04.2022
Revised: 10.10.2022
Accepted: 10.10.2022
English version:
Theory of Probability and its Applications, 2023, Volume 68, Issue 1, Pages 31–45
DOI: https://doi.org/10.1137/S0040585X97T99126X
Bibliographic databases:
Document Type: Article
MSC: 93E20 49N10 60H10
Language: Russian
Citation: E. S. Palamarchuk, “Optimal linear-quadratic regulator for a stochastic system under mutually inverse time preferences in the cost”, Teor. Veroyatnost. i Primenen., 68:1 (2023), 38–56; Theory Probab. Appl., 68:1 (2023), 31–45
Citation in format AMSBIB
\Bibitem{Pal23}
\by E.~S.~Palamarchuk
\paper Optimal linear-quadratic regulator for a~stochastic system under mutually inverse time preferences in the cost
\jour Teor. Veroyatnost. i Primenen.
\yr 2023
\vol 68
\issue 1
\pages 38--56
\mathnet{http://mi.mathnet.ru/tvp5567}
\crossref{https://doi.org/10.4213/tvp5567}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4604489}
\transl
\jour Theory Probab. Appl.
\yr 2023
\vol 68
\issue 1
\pages 31--45
\crossref{https://doi.org/10.1137/S0040585X97T99126X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85166207661}
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  • https://www.mathnet.ru/eng/tvp/v68/i1/p38
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