Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems
arXiv:1507.08133 · doi:10.1007/978-3-319-28028-8_10
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.
arXiv comment22 pages, 3 figures, 2 tables
References in corpus (10)
- Scroll waves in isotropic excitable media : linear instabilities, bifurcations and restabilized states
- Computation of the Drift Velocity of Spiral Waves using Response Functions
- Controlling the position of traveling waves in reaction-diffusion systems
- An analytical approach to initiation of propagating fronts
- Three-Dimensional Autonomous Pacemaker in the Photosensitive Belousov-Zhabotinsky medium
- Spatial Confinement Causes Lifetime Enhancement and Expansion of Vortex Rings with Positive Filament Tension
- Front propagation in three-dimensional corrugated reaction-diffusion media
- Shaping wave patterns in reaction-diffusion systems
- Stability of position control of traveling waves in reaction-diffusion systems
- Optimal trajectory tracking