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Structural, dynamical and symbolic observability: From dynamical systems to networks.

Luis A Aguirre1, Leonardo L Portes1,2, Christophe Letellier3

  • 1Programa de Pós-Graduação em Engenharia Elétrica, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil.

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This study explores continuous measures of observability in complex networks. It shows that network topology alone is insufficient, as dynamics and node coupling are crucial for ranking observability.

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Area of Science:

  • Systems Science
  • Network Theory
  • Control Theory

Background:

  • Classical observability is binary (observable/unobservable).
  • Observability is key for understanding complex networks.
  • Continuous measures for nonlinear dynamical systems emerged ~20 years ago.

Purpose of the Study:

  • Investigate established dynamical system observability concepts within network contexts.
  • Rank simple networks using continuous observability measures.
  • Highlight factors beyond topology influencing network observability.

Main Methods:

  • Extending dynamical system observability definitions to networks.
  • Utilizing continuous measures for quantitative observability assessment.
  • Employing numerical simulations for illustration and validation.

Main Results:

  • Networks can be ranked by observability using continuous measures.
  • Network topology alone is insufficient for determining observability.
  • System dynamics and node coupling significantly impact observability.

Conclusions:

  • Continuous observability measures offer nuanced insights into network properties.
  • A holistic approach considering dynamics and coupling is essential for network observability analysis.
  • This work provides a framework for assessing and comparing observability in networked systems.