Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems
Pattern Formation and Solitons
2016-04-25 v3 Mathematical Physics
math.MP
Adaptation and Self-Organizing Systems
Biological Physics
Chemical Physics
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.
Keywords
Cite
@article{arxiv.1507.08133,
title = {Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems},
author = {Christopher Ryll and Jakob Löber and Steffen Martens and Harald Engel and Fredi Tröltzsch},
journal= {arXiv preprint arXiv:1507.08133},
year = {2016}
}
Comments
22 pages, 3 figures, 2 tables