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Optimal control of the propagation of a graph in inhomogeneous media
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Deckelnick, Klaus, Elliott, Charles M. and Styles, Vanessa (2009) Optimal control of the propagation of a graph in inhomogeneous media. SIAM Journal on Control and Optimization, Vol.48 (No.3). pp. 1335-1352. doi:10.1137/080723648
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Official URL: http://dx.doi.org/10.1137/080723648
Abstract
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 $H^{-1}$-norm. We prove convergence of a discrete optimal control problem based on a monotone finite difference scheme and describe some numerical results.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Differential equations, Partial -- Research, Eikonal equation, Hamilton-Jacobi equations, Approximation theory | ||||
| Journal or Publication Title: | SIAM Journal on Control and Optimization | ||||
| Publisher: | Society for Industrial and Applied Mathematics | ||||
| ISSN: | 0363-0129 | ||||
| Official Date: | 15 April 2009 | ||||
| Dates: |
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| Volume: | Vol.48 | ||||
| Number: | No.3 | ||||
| Page Range: | pp. 1335-1352 | ||||
| DOI: | 10.1137/080723648 | ||||
| Status: | Peer Reviewed | ||||
| Access rights to Published version: | Open Access |
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