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Hamiltonian based a posteriori error estimation for Hamilton-Jacobi-Bellman equations

URN to cite this document: urn:nbn:de:bvb:703-epub-3578-5

Title data

Grüne, Lars ; Dower, Peter:
Hamiltonian based a posteriori error estimation for Hamilton-Jacobi-Bellman equations.
Bayreuth ; Melbourne , 2018 . - 3 S.

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Project information

Project title:
Project's official titleProject's id
No informationGR 1569/17-1

Project financing: Deutsche Forschungsgemeinschaft
Model predictive PDE control for energy efficient building operation: Economic model predictive control and time varying systems

Abstract

In this extended abstract we present a method for the a posteriori error estimation of the numerical solution to Hamilton-Jacobi-Bellman PDEs related to infinite horizon optimal control problems. The method uses the residual of the Hamiltonian, i.e., it checks how good the computed numerical solution satisfies the PDE and computes the difference between the numerical and the exact solution from this mismatch. We present results both for discounted and for undiscounted problems, which require different mathematical techniques. For discounted problems, an inherent contraction property can be used while for undiscounted problems an asymptotic stability property of the optimally controlled system is exploited.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): Extended Abstract
Keywords: Hamilton-Jacobi-Bellman equation; a posteriori error estimation; numerical solution
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-3578-5
Date Deposited: 12 Feb 2018 07:41
Last Modified: 28 Mar 2019 09:54
URI: https://epub.uni-bayreuth.de/id/eprint/3578

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