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

  • Christopher Ryll
  • Jakob Löber
  • Steffen MartensEmail author
  • Harald Engel
  • Fredi Tröltzsch
Chapter
Part of the Understanding Complex Systems book series (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.

Keywords

Optimal Control Problem Control Signal Spiral Wave Travel Wave Order Optimality Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Christopher Ryll
    • 1
  • Jakob Löber
    • 2
  • Steffen Martens
    • 2
    Email author
  • Harald Engel
    • 2
  • Fredi Tröltzsch
    • 1
  1. 1.Institut für Theoretische PhysikTechnische Universität BerlinBerlinGermany
  2. 2.Institut für Theoretische PhysikTechnische Universität BerlinBerlinGermany

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