A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces
Abstract
We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the socalled “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finitedimensional DREs converge to the solution of the infinitedimensional DRE. In addition, we prove that the optimal state and control of the approximate finitedimensional problem converge to the optimal state and control of the corresponding infinitedimensional problem.
 Authors:
 University of Innsbruck, Department of Mathematics (Austria)
 American University of Sharjah, Department of Mathematics (United Arab Emirates)
 Publication Date:
 OSTI Identifier:
 22617041
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Applied Mathematics and Optimization; Journal Volume: 75; Journal Issue: 3; Other Information: Copyright (c) 2017 Springer Science+Business Media New York; http://www.springerny.com; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; COMPUTER CALCULATIONS; CONTROL SYSTEMS; HILBERT SPACE; MANYDIMENSIONAL CALCULATIONS; MATHEMATICAL SOLUTIONS; PARTIAL DIFFERENTIAL EQUATIONS; RICCATI EQUATION; STOCHASTIC PROCESSES
Citation Formats
Levajković, Tijana, Email: tijana.levajkovic@uibk.ac.at, Email: t.levajkovic@sf.bg.ac.rs, Mena, Hermann, Email: hermann.mena@uibk.ac.at, and Tuffaha, Amjad, Email: atufaha@aus.edu. A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces. United States: N. p., 2017.
Web. doi:10.1007/S0024501693393.
Levajković, Tijana, Email: tijana.levajkovic@uibk.ac.at, Email: t.levajkovic@sf.bg.ac.rs, Mena, Hermann, Email: hermann.mena@uibk.ac.at, & Tuffaha, Amjad, Email: atufaha@aus.edu. A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces. United States. doi:10.1007/S0024501693393.
Levajković, Tijana, Email: tijana.levajkovic@uibk.ac.at, Email: t.levajkovic@sf.bg.ac.rs, Mena, Hermann, Email: hermann.mena@uibk.ac.at, and Tuffaha, Amjad, Email: atufaha@aus.edu. Thu .
"A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces". United States.
doi:10.1007/S0024501693393.
@article{osti_22617041,
title = {A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces},
author = {Levajković, Tijana, Email: tijana.levajkovic@uibk.ac.at, Email: t.levajkovic@sf.bg.ac.rs and Mena, Hermann, Email: hermann.mena@uibk.ac.at and Tuffaha, Amjad, Email: atufaha@aus.edu},
abstractNote = {We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the socalled “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finitedimensional DREs converge to the solution of the infinitedimensional DRE. In addition, we prove that the optimal state and control of the approximate finitedimensional problem converge to the optimal state and control of the corresponding infinitedimensional problem.},
doi = {10.1007/S0024501693393},
journal = {Applied Mathematics and Optimization},
number = 3,
volume = 75,
place = {United States},
year = {Thu Jun 15 00:00:00 EDT 2017},
month = {Thu Jun 15 00:00:00 EDT 2017}
}

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