# Control of traveling localized spots

Source: [Control of traveling localized spots](<https://www.sota2.com/research/paper/68fa38641e209131ce8ba2ad>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T03:53:38.277Z

Authors: Steffen Martens, Christopher Ryll, Jakob L\\"ober, Fredi Tr\\"oltzsch, Harald Engel

Published: 2017-03-13T04:39:02.000Z

## Abstract

Traveling localized spots represent an important class of self-organized two-dimensional patterns in reaction-diffusion systems. We study open-loop control intended to guide a stable spot along a desired trajectory with desired velocity. Simultaneously, the spot's concentration profile does not change under control. For a given protocol of motion, we first express the control signal analytically in terms of the Goldstone modes and the propagation velocity of the uncontrolled spot. Thus, detailed information about the underlying nonlinear reaction kinetics is unnecessary. Then, we confirm the optimality of this solution by demonstrating numerically its equivalence to the solution of a regularized, optimal control problem. To solve the latter, the analytical expressions for the control are excellent initial guesses speeding-up substantially the otherwise time-consuming calculations.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1703.04246>)

[PDF](<https://arxiv.org/pdf/1703.04246.pdf>)