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Control theory: history, mathematical achievements and perspectives


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dc.creator Fernández Cara, Enrique es
dc.creator Zuazua Iriondo, Enrique es 2016-05-20T06:58:28Z 2016-05-20T06:58:28Z 2003-12
dc.identifier.citation Fernández 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.issn 1575-9822 es
dc.description.abstract These 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.sponsorship Ministerio de Ciencia y Tecnología es
dc.format application/pdf es
dc.language.iso eng es
dc.publisher Sociedad Española de Matemática Aplicada es
dc.relation.ispartof Boletín de la Sociedad Española de Matemática Aplicada, 26, 79-140.
dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internacional *
dc.rights.uri *
dc.subject Control Theory es
dc.subject optimal control es
dc.subject controllability es
dc.subject differential equations es
dc.subject feedback es
dc.subject Optimization es
dc.subject Calculus of Variations es
dc.title Control theory: history, mathematical achievements and perspectives es
dc.type info:eu-repo/semantics/article es
dc.type.version info:eu-repo/semantics/publishedVersion es
dc.rights.accessrights info:eu-repo/semantics/openAccess es
dc.contributor.affiliation Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico es
dc.relation.projectID BFM2000-1317 es
dc.relation.projectID BFM2002-03345 es
idus.format.extent 62 p. es
dc.journaltitle Boletín de la Sociedad Española de Matemática Aplicada es
dc.publication.volumen 26 es
dc.publication.initialPage 79 es
dc.publication.endPage 140 es
dc.contributor.funder Ministerio de Ciencia y Tecnología (MCYT). España
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