Observability of dynamical networks

• Autor(a) principal: Arthur Noronha Montanari
• 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
• topic: Observability; Dynamical networks; Structural systems; Sensor placement; Observer design; Engenharia elétrica; Controle automático; Redes elétricas; Detectores

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.