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

dc.contributorGómez Echavarría, Lina María
dc.contributorUniversidad Nacional de Colombia - Sede Medellín
dc.contributorGrupo de Investigación en Procesos Dinámicos-KALMAN
dc.creatorLópez Aguirre, Esteban
dc.date.accessioned2020-08-20T20:30:21Z
dc.date.accessioned2022-09-21T18:32:22Z
dc.date.available2020-08-20T20:30:21Z
dc.date.available2022-09-21T18:32:22Z
dc.date.created2020-08-20T20:30:21Z
dc.date.issued2020-03-19
dc.identifierhttps://repositorio.unal.edu.co/handle/unal/78117
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/3409227
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.
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.
dc.languageeng
dc.publisherMedellín - Minas - Doctorado en Ingeniería - Sistemas Energéticos
dc.publisherDepartamento de Procesos y Energía
dc.publisherUniversidad Nacional de Colombia - Sede Medellín
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dc.rightsAtribución-NoComercial 4.0 Internacional
dc.rightsAcceso abierto
dc.rightshttp://creativecommons.org/licenses/by-nc/4.0/
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rightsDerechos reservados - Universidad Nacional de Colombia
dc.titleA set-theoretic approach to the observability of dynamical systems with non-ideal sensors
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