{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T08:26:17Z","timestamp":1761294377784,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,10,7]],"date-time":"2021-10-07T00:00:00Z","timestamp":1633564800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["434434223"],"award-info":[{"award-number":["434434223"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>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\u2013slave configuration of two identical Gray\u2013Scott 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.<\/jats:p>","DOI":"10.3390\/systems9040071","type":"journal-article","created":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T21:45:32Z","timestamp":1633988732000},"page":"71","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Distributed Parameter State Estimation for the Gray\u2013Scott Reaction-Diffusion Model"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7799-5996","authenticated-orcid":false,"given":"Petro","family":"Feketa","sequence":"first","affiliation":[{"name":"Automation and Control Group, Kiel University, 24143 Kiel, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2710-1851","authenticated-orcid":false,"given":"Alexander","family":"Schaum","sequence":"additional","affiliation":[{"name":"Automation and Control Group, Kiel University, 24143 Kiel, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9175-2157","authenticated-orcid":false,"given":"Thomas","family":"Meurer","sequence":"additional","affiliation":[{"name":"Automation and Control Group, Kiel University, 24143 Kiel, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1016\/0009-2509(84)87017-7","article-title":"Autocatalytic reactions in the isothermal, continuous stirred tank reactor: Oscillations and instabilities in the system A+ 2B\u21923B; B\u2192C","volume":"39","author":"Gray","year":"1984","journal-title":"Chem. 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