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Ezequiel Bianco-Martinez1, Murilo S Baptista1, Christophe Letellier2

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Summary

This study introduces a symbolic observability coefficient to simplify analyzing complex dynamical systems from time series data. This method overcomes computational challenges with high-dimensional and rational systems.

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Area of Science:

  • Dynamical Systems Theory
  • Control Theory
  • Computational Mathematics

Background:

  • Observability is crucial for reconstructing system dynamics from time series.
  • Analytical computation of observability coefficients becomes intractable for high-dimensional or rational systems due to exponentially large polynomial functions.
  • Existing methods face significant computational challenges with increasing system complexity.

Purpose of the Study:

  • To introduce a novel symbolic observability coefficient for simplified analysis of complex dynamical systems.
  • To provide a computationally tractable method for assessing system observability from time series data.
  • To demonstrate the efficacy of the symbolic approach for high-dimensional and rational systems.

Main Methods:

  • Development of a symbolic observability coefficient based on symbolic computation.
  • Utilizing the determinant of the observability matrix for symbolic calculation.
  • Analytical computation of the symbolic coefficient for a five-dimensional rational system.

Main Results:

  • The symbolic observability coefficient offers a straightforward analytical computation.
  • The method effectively bypasses the exponential complexity of traditional polynomial approaches.
  • Successful demonstration on a five-dimensional rational system validates the approach.

Conclusions:

  • The symbolic observability coefficient provides an efficient and analytically tractable method for assessing system observability.
  • This approach significantly simplifies the analysis of complex dynamical systems, particularly those with high-dimensional and rational governing equations.
  • The findings pave the way for more accessible and scalable analysis of complex system dynamics.