Observability and synchronization of dynamical networks: a numerical study

• Ano de defesa: 2018
• Autor(a) principal: Arthur Noronha Montanari
• Orientador(a): Luis Antonio Aguirre
• Banca de defesa: Luciano Cunha de Araújo Pimenta, Leonardo Antônio Borges Tôrres
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Federal de Minas Gerais
• Programa de Pós-Graduação: Programa de Pós-Graduação em Engenharia Elétrica
• Departamento: ENG - DEPARTAMENTO DE ENGENHARIA ELÉTRICA
• País: Brasil
• Palavras-chave em Português: Observability; Synchronization; Dynamical network; Particle filter; Cluster synchronization; Lyapunov stability
• Link de acesso: http://hdl.handle.net/1843/36001

Fundamental properties and classic methods of control theory, such as the computation of the observability matrix of a dynamical system or the stability analysis by Lyapunov direct method, faces serious numerical and scalability issues before high-dimensional systems. This led to a renewed interest in literature under the context of large and complex network systems. In this work, we focus on the observability and synchronization properties of dynamical networks—that is, interconnected systems where each node is modeled as an individual dynamical system. For instance, the traditional problem of sensor (actuator) placement in a network can be assessed as an observability (controllability) problem: the choice of the optimal subset of nodes under which a given observability (controllability) metric of the network is maximized. The contributions of this work in the context of observability of network systems are twofold: we review several proposed metric to quantify in a gradual manner the observability of dynamical and network systems; and, noticing a lack of validation in most works, we develop a Bayesian filtering framework, based on particle filtering, for application as a benchmark in observability studies. As shown, the particle filtering can also be used as a means to investigate the interplay between nodal dynamics and the network topology. Numerical results shows the effectiveness of this framework as performance metric for observability in network systems. On the other hand, in the context of synchronization, we investigate the theoretical sufficient conditions for phase synchronization between two interconnected “bridge oscillators” from different clusters of Kuramoto oscillators. In contrast to most graph-theoretical methods in literature, we take a reductionist approach that does not rely on full information of the adjacency matrix—which might be useful since this information is unavailable in some applications. The derived theoretical conditions are compared to numerical simulations. Finally, a brief insight for observability quantification in network systems is suggested in the conclusion.