Optimal boundary control of the wave equation with pointwise control constraints

Journal article
(Original article)


Publication Details

Author(s): Gugat M, Grimm V
Journal: Computational Optimization and Applications
Publisher: Springer Verlag (Germany)
Publication year: 2011
Volume: 49
Journal issue: 1
Pages range: 123-147
ISSN: 0926-6003
Language: English


Abstract


In optimal control problems frequently pointwise control constraints appear. We consider a finite string that is fixed at one end and controlled via Dirichlet conditions at the other end with a given upper bound M for the L -norm of the control. The problem is to control the string to the zero state in a given finite time. If M is too small, no feasible control exists. If M is large enough, the optimal control problem to find an admissible control with minimal L 2-norm has a solution that we present in this paper. A finite difference discretization of the optimal control problem is considered and we prove that for Lipschitz continuous data the discretization error is of the order of the stepsize. © 2009 Springer Science+Business Media, LLC.



FAU Authors / FAU Editors

Gugat, Martin apl. Prof. Dr.
Lehrstuhl für Angewandte Mathematik


External institutions with authors

Karlsruhe Institute of Technology (KIT)


How to cite

APA:
Gugat, M., & Grimm, V. (2011). Optimal boundary control of the wave equation with pointwise control constraints. Computational Optimization and Applications, 49(1), 123-147. https://dx.doi.org/10.1007/s10589-009-9289-7

MLA:
Gugat, Martin, and Volker Grimm. "Optimal boundary control of the wave equation with pointwise control constraints." Computational Optimization and Applications 49.1 (2011): 123-147.

BibTeX: 

Last updated on 2018-07-08 at 02:26