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 Avtomat. i Telemekh., 2013, Issue 4, Pages 110–128 (Mi at4977)

Stochastic Systems, Queuing Systems

On stochastic optimality for a linear controller with attenuating disturbances

T. A. Belkina, E. S. Palamarchuk

Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia

Abstract: For a linear stochastic control system with quadratic objective functional, we introduce various generalizations of the notions of optimality on average and stochastic optimality on an infinite time interval that take into account possible degeneration of the parameter of the disturbing process with time (attenuation of the disturbances) or the presence of a discount function in the objective functional. This lets us improve upon the quality estimate for a well known optimal control in this problem from the point of view of both asymptotic behavior of the functional's expectation and its asymptotic probabilistic properties. In particular, in the considered case we have found an improvement for the well known logarithmic upper bound on the optimal control for a family of defect processes.

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English version:
Automation and Remote Control, 2013, 74:4, 628–641

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Presented by the member of Editorial Board: À. Â. Íàçèí

Citation: T. A. Belkina, E. S. Palamarchuk, “On stochastic optimality for a linear controller with attenuating disturbances”, Avtomat. i Telemekh., 2013, no. 4, 110–128; Autom. Remote Control, 74:4 (2013), 628–641

Citation in format AMSBIB
\Bibitem{BelPal13} \by T.~A.~Belkina, E.~S.~Palamarchuk \paper On stochastic optimality for a~linear controller with attenuating disturbances \jour Avtomat. i Telemekh. \yr 2013 \issue 4 \pages 110--128 \mathnet{http://mi.mathnet.ru/at4977} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3216542} \zmath{https://zbmath.org/?q=an:1275.93064} \transl \jour Autom. Remote Control \yr 2013 \vol 74 \issue 4 \pages 628--641 \crossref{https://doi.org/10.1134/S0005117913040061} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000317624600006} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84876475112} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. E. S. Palamarchuk, “Asymptotic behavior of the solution to a linear stochastic differential equation and almost sure optimality for a controlled stochastic process”, Comput. Math. Math. Phys., 54:1 (2014), 83–96
2. E. S. Palamarchuk, “Stabilization of linear stochastic systems with a discount: modeling and estimation of the long-term effects from the application of optimal control strategies”, Math. Models Comput. Simul., 7:4 (2015), 381–388
3. E. S. Palamarchuk, “Stochastic optimality in the portfolio tracking problem involving investor's temporal preferences”, Autom. Remote Control, 78:8 (2017), 1523–1536
4. E. S. Palamarchuk, “Analysis of criteria for long-run average in the problem of stochastic linear regulator”, Autom. Remote Control, 77:10 (2016), 1756–1767
5. E. Palamarchuk, “On infinite time linear-quadratic gaussian control of inhomogeneous systems”, 2016 European Control Conference (Ecc), IEEE, 2016, 2477–2482
6. E. S. Palamarchuk, “Analysis of the asymptotic behavior of the solution to a linear stochastic differential equation with subexponentially stable matrix and its application to a control problem”, Theory Probab. Appl., 62:4 (2018), 522–533
7. E. S. Palamarchuk, “On the Generalization of Logarithmic Upper Function For Solution of a Linear Stochastic Differential Equation With a Nonexponentially Stable Matrix”, Differ. Equ., 54:2 (2018), 193–200
8. E. S. Palamarchuk, “An analytic study of the Ornstein–Uhlenbeck process with time-varying coefficients in the modeling of anomalous diffusions”, Autom. Remote Control, 79:2 (2018), 289–299
9. E. S. Palamarchuk, “Optimization of the superstable linear stochastic system applied to the model with extremely impatient agents”, Autom. Remote Control, 79:3 (2018), 439–450
10. E. S. Palamarchuk, “O zadache optimalnogo upravleniya lineinoi stokhasticheskoi sistemoi s neogranichennoi na beskonechnosti neustoichivoi matritsei sostoyaniya”, Avtomat. i telemekh., 2019, no. 2, 64–80
11. E. S. Palamarchuk, “O verkhnikh funktsiyakh dlya anomalnykh diffuzii, modeliruemykh protsessom Ornshteina–Ulenbeka s peremennymi koeffitsientami”, Teoriya veroyatn. i ee primen., 64:2 (2019), 258–282
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