Optimal Neumann boundary control of a vibrating string with uncertain initial data and probabilistic terminal constraints

Submission Status:in press
  • In optimal control problems, often initial data are required that are not known exactly in practice. In order to take into account this uncertainty, we consider optimal control problems for a system with an uncertain initial state. A finite terminal time is given. On account of the uncertainty of the initial state, it is not possible to prescribe an exact terminal state. Instead, we are looking for controls that steer the system into a given neighborhood of the desired terminal state with sufficiently high probability. This neighborhood is described in terms of an inequality for the terminal energy. The probabilistic constraint in the considered optimal control problem leads to optimal controls that are robust against the inevitable uncertainties of the initial state. We show the existence of such optimal controls. Numerical examples with optimal Neumann control of the wave equation are presented.

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Metadaten
Author:Mohammad Hassan Farshbaf Shaker, Martin Gugat, Holger Heitsch, René Henrion
DOI:https://doi.org/10.1137/19M1269944
Document Type:Article
Language:English
Date of Publication (online):2019/09/27
Release Date:2019/09/27
Tag:PDE constrained optimization, probabilistic constraints, uncertain initial data
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Weierstraß-Institut für Angewandte Analysis und Stochastik
Subprojects:B04
C03
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International
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