Optimal boundary control of the wave equation with pointwise control constraints

Gugat M, Grimm V (2011)


Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2011

Journal

Publisher: Springer Verlag (Germany)

Book Volume: 49

Pages Range: 123-147

Journal Issue: 1

URI: http://springerlink.com/content/k6345j348j147564/

DOI: 10.1007/s10589-009-9289-7

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.

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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.

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