Control of traveling localized spots
| dc.contributor.author | Martens, S. | |
| dc.contributor.author | Ryll, Christopher | |
| dc.contributor.author | Löber, Jakob | |
| dc.contributor.author | Tröltzsch, F. | |
| dc.contributor.author | Engel, Harald | |
| dc.date.accessioned | 2021-11-08T15:17:38Z | |
| dc.date.available | 2021-11-08T15:17:38Z | |
| dc.date.issued | 2021-07-26 | |
| dc.description.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. | en |
| dc.description.sponsorship | DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzepte | en |
| dc.identifier.eissn | 1760-6101 | |
| dc.identifier.issn | 0973-5348 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/13849 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-12625 | |
| dc.language.iso | en | en |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en |
| dc.subject.ddc | 510 Mathematik | de |
| dc.subject.other | pattern formation | en |
| dc.subject.other | Goldstone mode control | en |
| dc.subject.other | reaction–diffusion system | en |
| dc.subject.other | instabilities | en |
| dc.subject.other | traveling spot solutions | en |
| dc.title | Control of traveling localized spots | en |
| dc.type | Article | en |
| dc.type.version | publishedVersion | en |
| dcterms.bibliographicCitation.articlenumber | 46 | en |
| dcterms.bibliographicCitation.doi | 10.1051/mmnp/2021036 | en |
| dcterms.bibliographicCitation.issue | 46 | en |
| dcterms.bibliographicCitation.journaltitle | Mathematical Modelling of Natural Phenomena | en |
| dcterms.bibliographicCitation.originalpublishername | EDP Sciences | en |
| dcterms.bibliographicCitation.originalpublisherplace | Les Ulis | en |
| dcterms.bibliographicCitation.volume | 16 | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 5 Verkehrs- und Maschinensysteme::Inst. Mechanik::FG Mechatronische Maschinendynamik | de |
| tub.affiliation.faculty | Fak. 5 Verkehrs- und Maschinensysteme | de |
| tub.affiliation.group | FG Mechatronische Maschinendynamik | de |
| tub.affiliation.institute | Inst. Mechanik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |