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

This article is cited in 11 scientific papers (total in 11 papers)

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: А. В. Назин

Received: 14.08.2012

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
\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
\jour Autom. Remote Control
\yr 2013
\vol 74
\issue 4
\pages 628--641

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    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  mathnet  crossref  crossref  isi  elib  elib
    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  mathnet  crossref  mathscinet  elib
    3. E. S. Palamarchuk, “Stochastic optimality in the portfolio tracking problem involving investor's temporal preferences”, Autom. Remote Control, 78:8 (2017), 1523–1536  mathnet  crossref  elib
    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  mathnet  crossref  isi  elib
    5. E. Palamarchuk, “On infinite time linear-quadratic gaussian control of inhomogeneous systems”, 2016 European Control Conference (Ecc), IEEE, 2016, 2477–2482  crossref  isi
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    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  mathnet  crossref  mathscinet  zmath  isi  scopus
    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  mathnet  crossref  mathscinet  zmath  isi  elib
    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  mathnet  crossref  isi  elib
    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  mathnet  crossref  elib
    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  mathnet  crossref  elib
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