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arXiv · 1507.08133

Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems

Christopher Ryll·Jakob Löber·Steffen Martens·Harald Engel·Fredi Tröltzsch
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Abstract

This work deals with the position control of selected patterns in reaction-diffusion systems. Exemplarily, the Schl\"{o}gl and FitzHugh-Nagumo model are discussed using three different approaches. First, an analytical solution is proposed. Second, the standard optimal control procedure is applied. The third approach extends standard optimal control to so-called sparse optimal control that results in very localized control signals and allows the analysis of second order optimality conditions.

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Christopher Ryll, Jakob Löber, Steffen Martens, Harald Engel, Fredi Tröltzsch. 2015-07-29. Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems. https://doi.org/10.1007/978-3-319-28028-8_10

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