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dc.creatorFernández Cara, Enriquees
dc.creatorZuazua Iriondo, Enriquees
dc.date.accessioned2016-05-20T06:58:28Z
dc.date.available2016-05-20T06:58:28Z
dc.date.issued2003-12
dc.identifier.citationFernández Cara, E. y Zuazua Iriondo, E. (2003). Control theory: history, mathematical achievements and perspectives. Boletín de la Sociedad Española de Matemática Aplicada, 26, 79-140.
dc.identifier.issn1575-9822es
dc.identifier.urihttp://hdl.handle.net/11441/41421
dc.description.abstractThese notes are devoted to present some of the mathematical milestones of Control Theory. To do that, we first overview its origins and some of the main mathematical achievements. Then, we discuss the main domains of Sciences and Technologies where Control Theory arises and applies. This forces us to address modelling issues and to distinguish between the two main control theoretical approaches, controllability and optimal control, discussing the advantages and drawbacks of each of them. In order to give adequate formulations of the main questions, we have introduced some of the most elementary mathematical material, avoiding unnecessary technical difficulties and trying to make the paper accessible to a large class of readers. The subjects we address range from the basic concepts related to the dynamical systems approach to (linear and nonlinear) Mathematical Programming and Calculus of Variations. We also present a simplified version of the outstanding results by Kalman on the controllability of linear finite dimensional dynamical systems, Pontryaguin’s maximum principle and the principle of dynamical programming. Some aspects related to the complexity of modern control systems, the discrete versus continuous modelling, the numerical approximation of control problems and its control theoretical consequences are also discussed. Finally, we describe some of the major challenging applications in Control Theory for the XXI Century. They will probably influence strongly the development of this discipline in the near future.es
dc.description.sponsorshipMinisterio de Ciencia y Tecnologíaes
dc.formatapplication/pdfes
dc.language.isoenges
dc.publisherSociedad Española de Matemática Aplicadaes
dc.relation.ispartofBoletín de la Sociedad Española de Matemática Aplicada, 26, 79-140.
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectControl Theoryes
dc.subjectoptimal controles
dc.subjectcontrollabilityes
dc.subjectdifferential equationses
dc.subjectfeedbackes
dc.subjectOptimizationes
dc.subjectCalculus of Variationses
dc.titleControl theory: history, mathematical achievements and perspectiveses
dc.typeinfo:eu-repo/semantics/articlees
dc.type.versioninfo:eu-repo/semantics/publishedVersiones
dc.rights.accessrightsinfo:eu-repo/semantics/openAccesses
dc.contributor.affiliationUniversidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numéricoes
dc.relation.projectIDBFM2000-1317es
dc.relation.projectIDBFM2002-03345es
idus.format.extent62 p.es
dc.journaltitleBoletín de la Sociedad Española de Matemática Aplicadaes
dc.publication.volumen26es
dc.publication.initialPage79es
dc.publication.endPage140es
dc.identifier.idushttps://idus.us.es/xmlui/handle/11441/41421
dc.contributor.funderMinisterio de Ciencia y Tecnología (MCYT). España

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