A symbolic network-based nonlinear theory for dynamical systems observability

Christophe Letellier; Irene Sendiña-Nadal; Ezequiel Julian Bianco-Martinez; Murilo da Silva Baptista

doi:10.1038/s41598-018-21967-w

A symbolic network-based nonlinear theory for dynamical systems observability

Christophe Letellier, Irene Sendiña-Nadal, Ezequiel Julian Bianco-Martinez, Murilo da Silva Baptista

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Abstract

When the state of the whole reaction network can be inferred by just measuring the dynamics of a limited set of nodes the system is said to be fully observable. However, as the number of all possible combinations of measured variables and time derivatives spanning the reconstructed state of the system exponentially increases with its dimension, the observability becomes a computationally prohibitive task. Our approach consists in computing the observability coefficients from a symbolic Jacobian matrix whose elements encode the linear, nonlinear polynomial or rational nature of the interaction among the variables. The novelty we introduce in this paper, required for treating large-dimensional systems, is to identify from the symbolic Jacobian matrix the minimal set of variables (together with their time derivatives) candidate to be measured for completing the state space reconstruction. Then symbolic observability coefficients are computed from the symbolic observability matrix. Our results are in agreement with the analytical computations, evidencing the correctness of our approach. Its application to efficiently exploring the dynamics of real world complex systems such as power grids, socioeconomic networks or biological networks is quite promising.

Original language	English
Article number	3785
Pages (from-to)	1-15
Number of pages	15
Journal	Scientific Reports
Volume	8
DOIs	https://doi.org/10.1038/s41598-018-21967-w
Publication status	Published - 28 Feb 2018

Bibliographical note

EBM and MSB acknowledge the Engineering and Physical Sciences Research Council (EPSRC), grant Ref. EP/I032608/1. ISN acknowledges partial support from the Ministerio de Economía y Competitividad of Spain under project FIS2013-41057-P and from the Group of Research Excelence URJC-Banco de Santander.

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10.1038/s41598-018-21967-wLicence: CC BY

A symbolic network-based nonlinear theory for dynamical systems observability
© The Author(s) 2018 This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
Final published version, 1.3 MBLicence: CC BY

Murilo Baptista
- School of Natural & Computing Sciences, Physics - Reader
- Institute for Complex Systems and Mathematical Biology (ICSMB)
Person: Academic

Cite this

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title = "A symbolic network-based nonlinear theory for dynamical systems observability",

abstract = "When the state of the whole reaction network can be inferred by just measuring the dynamics of a limited set of nodes the system is said to be fully observable. However, as the number of all possible combinations of measured variables and time derivatives spanning the reconstructed state of the system exponentially increases with its dimension, the observability becomes a computationally prohibitive task. Our approach consists in computing the observability coefficients from a symbolic Jacobian matrix whose elements encode the linear, nonlinear polynomial or rational nature of the interaction among the variables. The novelty we introduce in this paper, required for treating large-dimensional systems, is to identify from the symbolic Jacobian matrix the minimal set of variables (together with their time derivatives) candidate to be measured for completing the state space reconstruction. Then symbolic observability coefficients are computed from the symbolic observability matrix. Our results are in agreement with the analytical computations, evidencing the correctness of our approach. Its application to efficiently exploring the dynamics of real world complex systems such as power grids, socioeconomic networks or biological networks is quite promising.",

author = "Christophe Letellier and Irene Sendi{\~n}a-Nadal and Bianco-Martinez, {Ezequiel Julian} and Baptista, {Murilo da Silva}",

note = "EBM and MSB acknowledge the Engineering and Physical Sciences Research Council (EPSRC), grant Ref. EP/I032608/1. ISN acknowledges partial support from the Ministerio de Econom{\'i}a y Competitividad of Spain under project FIS2013-41057-P and from the Group of Research Excelence URJC-Banco de Santander.",

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N1 - EBM and MSB acknowledge the Engineering and Physical Sciences Research Council (EPSRC), grant Ref. EP/I032608/1. ISN acknowledges partial support from the Ministerio de Economía y Competitividad of Spain under project FIS2013-41057-P and from the Group of Research Excelence URJC-Banco de Santander.

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A symbolic network-based nonlinear theory for dynamical systems observability

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