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Axioms 2019, 8(1), 30; https://doi.org/10.3390/axioms8010030

On the Linear Quadratic Optimal Control for Systems Described by Singularly Perturbed Itô Differential Equations with Two Fast Time Scales

Institute of Mathematics “Simion Stoilow” of the Romanian Academy, RO-014700 Bucharest, Romania
The author is a member of Academy of the Romanian Scientists.
Received: 15 January 2019 / Revised: 20 February 2019 / Accepted: 28 February 2019 / Published: 5 March 2019
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PDF [385 KB, uploaded 6 March 2019]

Abstract

In this paper a stochastic optimal control problem described by a quadratic performance criterion and a linear controlled system modeled by a system of singularly perturbed Itô differential equations with two fast time scales is considered. The asymptotic structure of the stabilizing solution (satisfying a prescribed sign condition) to the corresponding stochastic algebraic Riccati equation is derived. Furthermore, a near optimal control whose gain matrices do not depend upon small parameters is discussed. View Full-Text
Keywords: singularly perturbed linear stochastic systems; asymptotic structure of the stabilizing solution; optimal control problem; Riccati equations of stochastic control singularly perturbed linear stochastic systems; asymptotic structure of the stabilizing solution; optimal control problem; Riccati equations of stochastic control
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Drăgan, V. On the Linear Quadratic Optimal Control for Systems Described by Singularly Perturbed Itô Differential Equations with Two Fast Time Scales. Axioms 2019, 8, 30.

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