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Data-driven identification of dynamical models using adaptive parameter sets.

Dan Wilson1

  • 1Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, Tennessee 37996, USA.

Chaos (Woodbury, N.Y.)
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Summary
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This study introduces two advanced data-driven methods for identifying dynamical systems, outperforming existing techniques like DMDc for accurate model prediction.

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Area of Science:

  • Dynamical Systems Analysis
  • Model Identification
  • Control Theory

Background:

  • Accurate modeling of dynamical systems is crucial for prediction and control.
  • Existing data-driven methods like DMDc have limitations in handling complex dynamics.
  • Fixed point attractors and Koopman operator analysis are key concepts in system dynamics.

Purpose of the Study:

  • To present two novel data-driven model identification techniques for dynamical systems.
  • To improve accuracy and robustness in inferring dynamical models.
  • To compare the proposed methods against established algorithms.

Main Methods:

  • Development of two adaptive parameter update strategies for model identification.
  • Extension of the Dynamic Mode Decomposition with Control (DMDc) algorithm.
  • Utilizing a reduced-order isostable coordinate basis for Koopman operator analysis.

Main Results:

  • Both proposed techniques demonstrated superior accuracy and robustness.
  • The methods effectively captured the dynamics of systems near bifurcations and in complex flow scenarios.
  • Outperformed common algorithms including Koopman model predictive control, Galerkin projection, and DMDc.

Conclusions:

  • The novel data-driven methods offer significant improvements for dynamical system identification.
  • These techniques provide more reliable models for complex nonlinear systems.
  • The isostable coordinate approach shows promise for analyzing slow dynamics.