Observability of dynamical networks
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFMG |
Texto Completo: | http://hdl.handle.net/1843/36002 |
Resumo: | A quantitative understanding and precise control of a complex dynamical system, such as natural, social and technological networks, can only be achieved with the ability to observe its internal states either by direct measurement or indirect estimation. For a large-scale dynamical network, however, it is extremely difficult or physically impossible to place enough sensors to make the system fully observable. The problem of determining whether a system is observable has been well addressed by control engineers and, in a high-dimensional context, network scientists in the recent decade. Nevertheless, even if the system is theoretically observable, the high-dimensionality of the network poses fundamental limits on the computational tractability and performance of a full-state observer. To overcome the curse of dimensionality, and noting the fact that often only a small number of state variables in a network are essential for control, intervention, and monitoring purposes, we instead ask the system to be functionally observable, i.e., that only a targeted subset of system states be reconstructable from the available measurements. In this manuscript, we develop a graph-based theory of functional observability, which leads to highly scalable algorithms to determine minimal necessary sensors and to design the corresponding state observer with minimal order. Compared with the full-state observer, the developed functional observer achieves the same estimation quality with much less sensory and computational resources, making it applicable to large-scale networks. We apply the proposed methods to the detection of cyber-attacks in power grids under limited measurement units and the inference of the infected population during a pandemic under limited testing resources. The applications and numerical results show that the functional observer can significantly scale up our ability to explore otherwise hidden dynamical processes on large-scale complex networks. |
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Luis Antonio Aguirrehttp://lattes.cnpq.br/6682146998710900Elbert Einstein Nehrer MacauAdilson Enio MotterErivelton Geraldo NepomucenoLeonardo Antônio Borges Tôrreshttp://lattes.cnpq.br/2962992091083183Arthur Noronha Montanari2021-05-19T17:32:42Z2021-05-19T17:32:42Z2021-02-26http://hdl.handle.net/1843/36002A quantitative understanding and precise control of a complex dynamical system, such as natural, social and technological networks, can only be achieved with the ability to observe its internal states either by direct measurement or indirect estimation. For a large-scale dynamical network, however, it is extremely difficult or physically impossible to place enough sensors to make the system fully observable. The problem of determining whether a system is observable has been well addressed by control engineers and, in a high-dimensional context, network scientists in the recent decade. Nevertheless, even if the system is theoretically observable, the high-dimensionality of the network poses fundamental limits on the computational tractability and performance of a full-state observer. To overcome the curse of dimensionality, and noting the fact that often only a small number of state variables in a network are essential for control, intervention, and monitoring purposes, we instead ask the system to be functionally observable, i.e., that only a targeted subset of system states be reconstructable from the available measurements. In this manuscript, we develop a graph-based theory of functional observability, which leads to highly scalable algorithms to determine minimal necessary sensors and to design the corresponding state observer with minimal order. Compared with the full-state observer, the developed functional observer achieves the same estimation quality with much less sensory and computational resources, making it applicable to large-scale networks. We apply the proposed methods to the detection of cyber-attacks in power grids under limited measurement units and the inference of the infected population during a pandemic under limited testing resources. The applications and numerical results show that the functional observer can significantly scale up our ability to explore otherwise hidden dynamical processes on large-scale complex networks.A compreensão quantitativa e controle preciso de um sistema dinâmico complexo, como redes naturais, sociais e tecnológicas, podem ser alcançadas apenas com a habilidade de observar seus estados internos, seja por meio de medições diretas ou estimação indireta. No caso de uma rede dinâmica de larga-escala, entretanto, é extremamente difícil ou fisicamente impossível alocar um número suficiente de sensores para tornar um sistema completamente observável. O problema de determinar se um sistema é observável foi intensivamente estudado por engenheiros de controle e, no contexto de alta-dimensionalidade, cientistas de redes na década recente. Não obstante, mesmo se um sistema for teoricamente observável, a alta-dimensionalidade de redes apresenta limites fundamentais à tratabilidade computacional e desempenho de um observador de estados completo. Com o objetivo de superar a maldição da dimensionalidade, e notando o fato que usualmente apenas um pequeno subconjunto das variáveis de estado em uma rede são essenciais para propósitos de controle, intervenção e monitoramento, investiga-se nesta tese as condições para que um sistema seja observável funcional, isto é, que apenas um subconjunto alvo dos estados do sistema sejam reconstrutíveis a partir das medições disponíveis. Neste manuscrito, desenvolve-se uma teoria baseada em grafos da propriedade de observabilidade funcional, que permite o desenvolvimento de algoritmos altamente escaláveis para a determinação do conjunto mínimo necessário de sensores e o projeto de um observador de estados funcional de mínima ordem. Comparado ao observador de estados completo, o observador de estados funcional apresenta a mesma qualidade na estimação de estados com muito menos recursos sensoriais e computacionais, tornando-o adequado à aplicações em redes de larga-escala. Os métodos propostos são aplicados na detecção de ataques cibernéticos em redes de potência sob um limitado número de unidades de medição, e na inferência das populações infectadas durante uma epidemia sob capacidade limitada de testes. As aplicações e resultados numéricos mostram que o observador de estados funcional pode aumentar significativamente nossa habilidade de explorar processos dinâmicos ocultos em redes complexas de larga-escala.CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorengUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em Engenharia ElétricaUFMGBrasilENG - DEPARTAMENTO DE ENGENHARIA ELÉTRICAEngenharia elétricaControle automáticoRedes elétricasDetectoresObservabilityDynamical networksStructural systemsSensor placementObserver designObservability of dynamical networksObservabilidade de redes dinâmicasinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGORIGINALTese de Doutorado - Arthur Montanari - Versão Biblioteca.pdfTese de Doutorado - Arthur Montanari - Versão Biblioteca.pdfTese de doutoradoapplication/pdf3108241https://repositorio.ufmg.br/bitstream/1843/36002/1/Tese%20de%20Doutorado%20-%20Arthur%20Montanari%20-%20Vers%c3%a3o%20Biblioteca.pdf2459160330f00ff0237a752f48647396MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-82119https://repositorio.ufmg.br/bitstream/1843/36002/2/license.txt34badce4be7e31e3adb4575ae96af679MD521843/360022021-05-19 14:32:42.227oai:repositorio.ufmg.br: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Repositório de PublicaçõesPUBhttps://repositorio.ufmg.br/oaiopendoar:2021-05-19T17:32:42Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false |
dc.title.pt_BR.fl_str_mv |
Observability of dynamical networks |
dc.title.alternative.pt_BR.fl_str_mv |
Observabilidade de redes dinâmicas |
title |
Observability of dynamical networks |
spellingShingle |
Observability of dynamical networks Arthur Noronha Montanari Observability Dynamical networks Structural systems Sensor placement Observer design Engenharia elétrica Controle automático Redes elétricas Detectores |
title_short |
Observability of dynamical networks |
title_full |
Observability of dynamical networks |
title_fullStr |
Observability of dynamical networks |
title_full_unstemmed |
Observability of dynamical networks |
title_sort |
Observability of dynamical networks |
author |
Arthur Noronha Montanari |
author_facet |
Arthur Noronha Montanari |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Luis Antonio Aguirre |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/6682146998710900 |
dc.contributor.referee1.fl_str_mv |
Elbert Einstein Nehrer Macau |
dc.contributor.referee2.fl_str_mv |
Adilson Enio Motter |
dc.contributor.referee3.fl_str_mv |
Erivelton Geraldo Nepomuceno |
dc.contributor.referee4.fl_str_mv |
Leonardo Antônio Borges Tôrres |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/2962992091083183 |
dc.contributor.author.fl_str_mv |
Arthur Noronha Montanari |
contributor_str_mv |
Luis Antonio Aguirre Elbert Einstein Nehrer Macau Adilson Enio Motter Erivelton Geraldo Nepomuceno Leonardo Antônio Borges Tôrres |
dc.subject.por.fl_str_mv |
Observability Dynamical networks Structural systems Sensor placement Observer design |
topic |
Observability Dynamical networks Structural systems Sensor placement Observer design Engenharia elétrica Controle automático Redes elétricas Detectores |
dc.subject.other.pt_BR.fl_str_mv |
Engenharia elétrica Controle automático Redes elétricas Detectores |
description |
A quantitative understanding and precise control of a complex dynamical system, such as natural, social and technological networks, can only be achieved with the ability to observe its internal states either by direct measurement or indirect estimation. For a large-scale dynamical network, however, it is extremely difficult or physically impossible to place enough sensors to make the system fully observable. The problem of determining whether a system is observable has been well addressed by control engineers and, in a high-dimensional context, network scientists in the recent decade. Nevertheless, even if the system is theoretically observable, the high-dimensionality of the network poses fundamental limits on the computational tractability and performance of a full-state observer. To overcome the curse of dimensionality, and noting the fact that often only a small number of state variables in a network are essential for control, intervention, and monitoring purposes, we instead ask the system to be functionally observable, i.e., that only a targeted subset of system states be reconstructable from the available measurements. In this manuscript, we develop a graph-based theory of functional observability, which leads to highly scalable algorithms to determine minimal necessary sensors and to design the corresponding state observer with minimal order. Compared with the full-state observer, the developed functional observer achieves the same estimation quality with much less sensory and computational resources, making it applicable to large-scale networks. We apply the proposed methods to the detection of cyber-attacks in power grids under limited measurement units and the inference of the infected population during a pandemic under limited testing resources. The applications and numerical results show that the functional observer can significantly scale up our ability to explore otherwise hidden dynamical processes on large-scale complex networks. |
publishDate |
2021 |
dc.date.accessioned.fl_str_mv |
2021-05-19T17:32:42Z |
dc.date.available.fl_str_mv |
2021-05-19T17:32:42Z |
dc.date.issued.fl_str_mv |
2021-02-26 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1843/36002 |
url |
http://hdl.handle.net/1843/36002 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Minas Gerais |
dc.publisher.program.fl_str_mv |
Programa de Pós-Graduação em Engenharia Elétrica |
dc.publisher.initials.fl_str_mv |
UFMG |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
ENG - DEPARTAMENTO DE ENGENHARIA ELÉTRICA |
publisher.none.fl_str_mv |
Universidade Federal de Minas Gerais |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFMG instname:Universidade Federal de Minas Gerais (UFMG) instacron:UFMG |
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UFMG |
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UFMG |
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Repositório Institucional da UFMG |
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Repositório Institucional da UFMG |
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