A set-theoretic approach to the observability of dynamical systems with non-ideal sensors

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dc.contributor.advisorGómez Echavarría, Lina Maríaspa
dc.contributor.authorLópez Aguirre, Estebanspa
dc.contributor.corporatenameUniversidad Nacional de Colombia - Sede Medellínspa
dc.contributor.researchgroupGrupo de Investigación en Procesos Dinámicos-KALMANspa
dc.date.accessioned2020-08-20T20:30:21Zspa
dc.date.available2020-08-20T20:30:21Zspa
dc.date.issued2020-03-19spa
dc.description.abstractEsta disertación propone un nuevo enfoque para la observabilidad de sistemas dinámicos basado en herramientas de la teoría de conjuntos. Este enfoque posee las ventajas de tener en cuenta la incertidumbre de las mediciones, conducir a una forma intuitiva de cuantificar la observabilidad, estar formalmente relacionado con la exactitud de la estimación de estado y ser fácilmente aplicado a sistemas no lineales y discretos. Con base en este formalismo se presenta un índice de observabilidad y se propone una versión promedio aproximada de este índice para obtener una cuantificación que sea independiente de las entradas aplicadas. La validez de la propuesta y su relación con la exactitud de la estimación de estado se demuestra mediante argumentos matemáticos rigurosos y se evidencia por medio de un ejemplo abstracto. Finalmente, se describen y se ilustran mediante simulaciones algunas aplicaciones del enfoque desarrollado al diseño y al control automático, mostrando que dicho enfoque es una herramienta útil para tareas que apuntan al incremento de la exactitud de la estimación de estado.spa
dc.description.abstractThis dissertation proposes a new approach to the observability of dynamical systems based on set-theoretic tools. This approach has the advantages of taking measurement uncertainty into account, leading to a straightforward way of quantifying observability, being formally related to state estimation accuracy, and being easily applied to nonlinear and discrete-time systems. Based on this formalism, an observability index is also introduced, and an approximate average version of this index is proposed in order to obtain a quantification that is independent from the applied inputs. The validity of the proposal and its relation to state estimation accuracy is supported through rigorous mathematical arguments and demonstrated by means of an abstract example. Finally, some applications of the devised approach to design and control are described and illustrated via simulation, showing that said approach is a useful tool for tasks aiming at enhancing state estimation accuracy.spa
dc.description.degreelevelDoctoradospa
dc.format.extent91spa
dc.format.mimetypeapplication/pdfspa
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/78117
dc.language.isoengspa
dc.publisher.branchUniversidad Nacional de Colombia - Sede Medellínspa
dc.publisher.departmentDepartamento de Procesos y Energíaspa
dc.publisher.programMedellín - Minas - Doctorado en Ingeniería - Sistemas Energéticosspa
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dc.rightsDerechos reservados - Universidad Nacional de Colombiaspa
dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.rights.licenseAtribución-NoComercial 4.0 Internacionalspa
dc.rights.spaAcceso abiertospa
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0/spa
dc.subject.ddc620 - Ingeniería y operaciones afines::629 - Otras ramas de la ingenieríaspa
dc.subject.proposalmétodos de la teoría de conjuntosspa
dc.subject.proposalset-theoretic methodseng
dc.subject.proposalestimación de estadospa
dc.subject.proposalstate estimationeng
dc.subject.proposalinput trajectory designeng
dc.subject.proposaldiseño de trayectoria de entradaspa
dc.subject.proposalcontrol automáticospa
dc.subject.proposalautomatic controleng
dc.titleA set-theoretic approach to the observability of dynamical systems with non-ideal sensorsspa
dc.title.alternativeUn enfoque de la teoría de conjuntos para la observabilidad de sistemas dinámicos con sensores no idealesspa
dc.typeTrabajo de grado - Doctoradospa
dc.type.coarhttp://purl.org/coar/resource_type/c_db06spa
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aaspa
dc.type.contentTextspa
dc.type.driverinfo:eu-repo/semantics/doctoralThesisspa
dc.type.versioninfo:eu-repo/semantics/acceptedVersionspa
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2spa

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