A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces
- University of Innsbruck, Department of Mathematics (Austria)
- American University of Sharjah, Department of Mathematics (United Arab Emirates)
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 so-called “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 finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.
- OSTI ID:
- 22617041
- Journal Information:
- Applied Mathematics and Optimization, Vol. 75, Issue 3; Other Information: Copyright (c) 2017 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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