dc.creator | Fernández Cara, Enrique | es |
dc.creator | Zuazua Iriondo, Enrique | es |
dc.date.accessioned | 2016-05-20T06:58:28Z | |
dc.date.available | 2016-05-20T06:58:28Z | |
dc.date.issued | 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.identifier.uri | http://hdl.handle.net/11441/41421 | |
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 | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
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.identifier.idus | https://idus.us.es/xmlui/handle/11441/41421 | |
dc.contributor.funder | Ministerio de Ciencia y Tecnología (MCYT). España | |