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Observability of Dynamical Networks from Graphic and Symbolic Approaches

  • Irene Sendiña-Nadal
  • Christophe LetellierEmail author
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)

Abstract

A dynamical network, a graph whose nodes are dynamical systems, is usually characterized by a large dimensional space which is not always accessible due to the impossibility of measuring all the variables spanning the state space. Therefore, it is of the utmost importance to determine a reduced set of variables providing all the required information to non-ambiguously distinguish its different states. Inherited from control theory, one possible approach is based on the use of the observability matrix defined as the Jacobian matrix of the change of coordinates between the original state space and the space reconstructed from the measured variables. The observability of a given system can be accurately assessed by symbolically computing the complexity of the determinant of the observability matrix and quantified by symbolic observability coefficients. In this work, we extend the symbolic observability, previously developed for dynamical systems, to networks made of coupled d-dimensional node dynamics (d > 1). From the observability of the node dynamics, the coupling function between the nodes, and the adjacency matrix, it is indeed possible to construct the observability of a large network with an arbitrary topology.

Keywords

Dynamical network Observability 

Notes

Acknowledgements

ISN acknowledges partial support from the Ministerio de Economía y Competitividad of Spain under project FIS2017-84151-P and from the Group of Research Excelence URJC-Banco de Santander.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Complex Systems Group & GISCUniversidad Rey Juan CarlosMóstolesSpain
  2. 2.Center for Biomedical TechnologyUniversidad Politécnica de MadridPozuelo de AlarcónSpain
  3. 3.Normandie Université CORIASaint-Etienne du RouvrayFrance

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