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Physics-informed data-driven control without persistence of excitation

(2025)

Paper Information
arXiv ID
2504.08484
Venue
arXiv.org
Contents

Abstract

We show that data that is not sufficiently informative to allow for system re-identification can still provide meaningful information when combined with external or physical knowledge of the system, such as bounded system matrix norms.We then illustrate how this information can be leveraged for safety and energy minimization problems and to enhance predictions in unmodelled dynamics.This preliminary work outlines key ideas toward using limited data for effective control by integrating physical knowledge of the system and exploiting interpolation conditions.

Summary

This paper explores a novel approach to data-driven control that operates without relying on the assumption of persistence of excitation. It suggests that even when data is insufficient for system re-identification, useful information can still be extracted through the integration of external or physical knowledge about the system, such as bounded matrix norms. The results indicate that when the system's matrix is bounded, the set of feasible states forms an ellipsoid, which is rigorously characterized. Applications of this framework include addressing safety and energy minimization problems, as well as enhancing predictions related to unmodelled dynamics. This work constitutes a significant step toward leveraging limited data in control scenarios by incorporating physical information and exploiting interpolation conditions, which promise to extend traditional data-driven methodologies, especially in linear time-invariant systems.

Methods

This paper employs the following methods:

  • Data-driven control
  • Linear time-invariant systems
  • Interpolation conditions

Models Used

  • None specified

Datasets

The following datasets were used in this research:

  • None specified

Evaluation Metrics

  • None specified

Results

  • Feasible states form an ellipsoid when the system's matrix is bounded.
  • Application in safety and energy minimization problems.
  • Enhancement of predictions in unmodelled dynamics.

Limitations

The authors identified the following limitations:

  • The work is preliminary and aims to combine physical knowledge with limited data without requiring assumptions about the amount of data.

Technical Requirements

  • Number of GPUs: None specified
  • GPU Type: None specified
  • Compute Requirements: None specified

Papers Using Similar Methods

External Resources

References: 22