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

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Control of Self-Organizing Nonlinear Systems

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

This work deals with the position control of selected patterns in reaction-diffusion systems. Exemplarily, the Schlögl 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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Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Technische Universität Berlin, 10623, Berlin, Germany

    Christopher Ryll & Fredi Tröltzsch

  2. Institut für Theoretische Physik, Technische Universität Berlin, 10623, Berlin, Germany

    Jakob Löber, Steffen Martens & Harald Engel

Authors
  1. Christopher Ryll
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  2. Jakob Löber
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  3. Steffen Martens
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  4. Harald Engel
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  5. Fredi Tröltzsch
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Corresponding author

Correspondence to Steffen Martens .

Editor information

Editors and Affiliations

  1. Inst für Theoretische Physik, Technische Universität Berlin, Berlin, Berlin, Germany

    Eckehard Schöll

  2. Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany

    Sabine H. L. Klapp

  3. Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany

    Philipp Hövel

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Ryll, C., Löber, J., Martens, S., Engel, H., Tröltzsch, F. (2016). Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems. In: Schöll, E., Klapp, S., Hövel, P. (eds) Control of Self-Organizing Nonlinear Systems. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-28028-8_10

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