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Distributed Parameter State Estimation for the Gray–Scott Reaction-Diffusion Model

Feketa, Petro; Schaum, Alexander ; Meurer, Thomas ORCID iD icon


A constructive approach is provided for the reconstruction of stationary and non-stationary patterns in the one-dimensional Gray-Scott model, utilizing measurements of the system state at a finite number of locations. Relations between the parameters of the model and the density of the sensor locations are derived that ensure the exponential convergence of the estimated state to the original one. The designed observer is capable of tracking a variety of complex spatiotemporal behaviors and self-replicating patterns. The theoretical findings are illustrated in particular numerical case studies. The results of the paper can be used for the synchronization analysis of the master–slave configuration of two identical Gray–Scott models coupled via a finite number of spatial points and can also be exploited for the purposes of feedback control applications in which the complete state information is required.

Verlagsausgabe §
DOI: 10.5445/IR/1000156588
Veröffentlicht am 10.03.2023
DOI: 10.3390/systems9040071
Zitationen: 4
Zitationen: 5
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Mechanische Verfahrenstechnik und Mechanik (MVM)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2021
Sprache Englisch
Identifikator ISSN: 2079-8954
KITopen-ID: 1000156588
Erschienen in Systems
Verlag MDPI
Band 9
Heft 4
Seiten Art.-Nr.: 71
Vorab online veröffentlicht am 07.10.2021
Schlagwörter Gray–Scott model, observer design, pattern formation, reaction diffusion equations
Nachgewiesen in Dimensions
Web of Science
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