Optimal Control of the Propagation of a Graph in Inhomogeneous Media

We study an optimal control problem for viscosity solutions of a Hamilton-Jacobi equation describing the propagation of a one-dimensional graph with the control being the speed function. The existence of an optimal control is proved together with an approximate controllability result in the H^sup -1...

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Bibliographic Details
Published in:SIAM journal on control and optimization 2009-01, Vol.48 (3), p.1335-1352
Main Authors: Deckelnick, Klaus, Elliott, Charles M, Styles, Vanessa
Format: Article
Language:English
Subjects:
Approximation
Controllability
Convergence
Graphs
Inhomogeneous media
Mathematical analysis
Mathematical models
Optimal control
Optimization
Studies
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Summary:We study an optimal control problem for viscosity solutions of a Hamilton-Jacobi equation describing the propagation of a one-dimensional graph with the control being the speed function. The existence of an optimal control is proved together with an approximate controllability result in the H^sup -1^-norm. We prove convergence of a discrete optimal control problem based on a monotone finite difference scheme and describe some numerical results. [PUBLICATION ABSTRACT]
ISSN:0363-0129
1095-7138
DOI:10.1137/080723648