{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T10:44:21Z","timestamp":1709203461817},"reference-count":29,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010,9,1]]},"abstract":"<jats:title>Protector control: Extension to a class of nonlinear distributed systems<\/jats:title><jats:p>We present an extension of the protector control scheme introduced for the linear case in a previous work to a class of nonlinear systems. The systems considered are assumed to have a finite propagation velocity while the initial state is subject to a spreading disturbance. We characterize such a control first by using the remediability approach to the resulting nonlinear delay system, and then by coupling families of transformations and the delay approach. To illustrate this work, we provide a simulation example.<\/jats:p>","DOI":"10.2478\/v10006-010-0032-4","type":"journal-article","created":{"date-parts":[[2010,9,28]],"date-time":"2010-09-28T01:01:44Z","timestamp":1285635704000},"page":"427-443","source":"Crossref","is-referenced-by-count":4,"title":["Protector control: Extension to a class of nonlinear distributed systems"],"prefix":"10.61822","volume":"20","author":[{"given":"Youssef","family":"Qaraai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdes","family":"Bernoussi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"37438","reference":[{"issue":"4","key":"1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/002077202317216884","article-title":"Regionally efficient and strategic actuators","volume":"33","author":"L. Afifi","year":"2002","journal-title":"International Journal of Systems Science"},{"issue":"2","key":"2","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1080\/002077200291262","article-title":"Detection and sources reconstruction in a tube","volume":"31","author":"L. Afifi","year":"2000","journal-title":"International Journal of Systems Science"},{"issue":"2","key":"3","first-page":"319","article-title":"Regional detection and reconstruction of unknown internal or boundary sources","volume":"11","author":"L. Afifi","year":"2001","journal-title":"International Journal of Applied Mathematics and Computer Science"},{"key":"4","volume-title":"Mathematics for Dynamic Modelling","author":"E. Beltrami","year":"1987"},{"issue":"4","key":"5","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1080\/00207720601159787","article-title":"Spreadability and vulnerability of distributed parameter systems","volume":"38","author":"A. Bernoussi","year":"2007","journal-title":"International Journal of Systems Science"},{"issue":"4","key":"6","first-page":"53","article-title":"Etalabilit\u00e9\u2014vulnrabilit\u00e9","volume":"30","author":"A. Bernoussi","year":"2003","journal-title":"Annals of University of Craiova"},{"issue":"13","key":"7","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/S0895-7177(00)00114-X","article-title":"New approach of spreadability","volume":"31","author":"A. Bernoussi","year":"2000","journal-title":"Journal of Mathematical and Computer Modelling"},{"issue":"10","key":"8","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1080\/00207720110035246","article-title":"Spreadability and evolving interfaces","volume":"32","author":"A. Bernoussi","year":"2001","journal-title":"International Journal of Systems Science"},{"issue":"7","key":"9","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1051\/mmnp\/20105724","article-title":"Spreadability, vulnerability and protector control","volume":"5","author":"A. Bernoussi","year":"2010","journal-title":"Mathematical Modelling of Natural Phenomena"},{"key":"10","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0006761","volume-title":"Infinite Dimensional Linear Systems Theory","author":"R. Curtain","year":"1978"},{"key":"11","volume-title":"Analyse math\u00e9matique et calcul num\u00e9rique pour les sciences et les techniques","author":"R. Dautray","year":"1984"},{"key":"12","volume-title":"Mathematics Climate and Environment","author":"J. Diaz","year":"1993"},{"key":"13","first-page":"663","article-title":"Analyse r\u00e9gionale des syst\u00e9mes distribu\u00e8s, SMAI (Soci\u00e9t\u00e9 de Math\u00e9matiques Appliqu\u00e9es et Industrielles)","volume":"8","author":"A. El Jai","year":"2002","journal-title":"ESAIM\u2014European Series in Applied and Industrial Mathematics"},{"key":"14","volume-title":"El\u00e9ments d'Analyse et Contr\u00f4le des Syst\u00e8mes","author":"A. El Jai","year":"2004"},{"issue":"1","key":"15","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/0895-7177(94)90218-6","article-title":"Spreadable distributed systems","volume":"20","author":"A. El Jai","year":"1994","journal-title":"Mathematical and Computer Modelling"},{"issue":"7","key":"16","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1080\/00207729608929265","article-title":"Spreadability of transport systems","volume":"27","author":"A. El Jai","year":"1996","journal-title":"International Journal of Systems Science"},{"key":"17","volume-title":"Capteurs et actionneurs dans l'analyse des systems distribu\u00e9s","author":"A. El Jai","year":"1986"},{"issue":"6","key":"18","doi-asserted-by":"crossref","first-page":"1351","DOI":"10.1080\/00207179508921603","article-title":"Regional controllability of distributed systems","volume":"62","author":"A. El Jai","year":"1995","journal-title":"International Journal of Control"},{"key":"19","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/S0167-2789(03)00176-3","article-title":"Analytic solutions of a nonlinear convective equation in population dynamics","volume":"183","author":"L. Giuggioli","year":"2003","journal-title":"Physica D"},{"key":"20","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0089647","volume-title":"Geometric Theory of Semilinear Parabolic Systems","volume":"840","author":"D. Henry","year":"1981"},{"issue":"5","key":"21","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1137\/0320048","article-title":"Quadratic control of evolution equations with delays in control","volume":"20","author":"A. Ichikawa","year":"1982","journal-title":"SIAM Journal Control and Optimization"},{"key":"22","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.physa.2004.04.084","article-title":"Results from variants of the Fisher equation in the study of epidemics and bacteria","volume":"342","author":"V. Kenkre","year":"2004","journal-title":"Physica A"},{"key":"23","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-5561-1","volume-title":"Semigroups of Linear Operators and Applications to Partial Differential Equations","volume":"44","author":"A. Pazy","year":"1983"},{"key":"24","unstructured":"Qaraai, Y. (2008). <i>Compensation des perturbations \u00e9talables et contr\u00f4le protecteur des zones vulnrables<\/i>, Ph.D. thesis, Faculty of Sciences and Techniques of Tangier, Morocco."},{"key":"25","first-page":"108","article-title":"Contr\u00f4le protecteur et remdiabilit\u00e9","author":"Y. Qaraai","year":"2006"},{"issue":"2","key":"26","doi-asserted-by":"publisher","first-page":"171","DOI":"10.2478\/v10006-008-0016-9","article-title":"How to compensate a spreading disturbance for a class of nonlinear systems","volume":"18","author":"Y. Qaraai","year":"2008","journal-title":"International Journal Applied Mathematics and Computer Science"},{"key":"27","first-page":"265","article-title":"Protector control for a class of nonlinear systems","author":"Y. Qaraai","year":"2009"},{"key":"28","volume-title":"Fixed Point Theorems","author":"D. Smart","year":"1994"},{"issue":"6","key":"29","first-page":"301","article-title":"Regional observability of distributed systems","volume":"25","author":"E. Zerrik","year":"1994","journal-title":"International Journal of Systems Science"}],"container-title":["International Journal of Applied Mathematics and Computer Science"],"original-title":[],"link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/amcs\/20\/3\/article-p427.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/amcs.2010.20.issue-3\/v10006-010-0032-4\/v10006-010-0032-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T10:27:51Z","timestamp":1709202471000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/v10006-010-0032-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9,1]]},"references-count":29,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.2478\/v10006-010-0032-4","relation":{},"ISSN":["1641-876X"],"issn-type":[{"value":"1641-876X","type":"print"}],"subject":[],"published":{"date-parts":[[2010,9,1]]}}}