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Evan Monroig1, Kazuyuki Aihara, Yozo Fujino

  • 1Department of Civil Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan. evan.monroig@m4x.org

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Summary

This study introduces a new method to reconstruct input-output systems using only output data, even when inputs are unmeasurable. This technique models system dynamics for applications like change detection and noise reduction.

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Area of Science:

  • Systems Engineering
  • Control Theory
  • Data Science

Background:

  • Reconstructing input-output systems from time series data is crucial for understanding complex dynamics.
  • Traditional methods like the method of delays require simultaneous measurement of both inputs and outputs.
  • Unmeasurable inputs pose a significant challenge for system identification.

Purpose of the Study:

  • To develop a novel approach for reconstructing input-output systems when inputs are unmeasurable.
  • To leverage multivariate output observations for system identification.
  • To explore applications in analyzing coupled systems and complex networks.

Main Methods:

  • Utilizing ideas from embedding theorems to construct models.
  • Employing delays of multivariate output observations to infer system states and inputs.
  • Assuming a limited number of inputs to facilitate information extraction from output data.

Main Results:

  • Demonstrated successful input-output system identification using only multivariate output data through numerical examples.
  • Validated the method on both discrete maps and continuous-time systems.
  • Showcased the applicability to analyzing subsystems within larger coupled systems or networks.

Conclusions:

  • Multivariate output observations are sufficient for reconstructing and modeling the dynamics of input-output systems, even with unmeasurable inputs.
  • The developed non-predictive models offer valuable applications in change detection and noise reduction.
  • This approach provides a robust framework for analyzing complex systems and networks by subsystem analysis.