Error bounds for port-Hamiltonian model and controller reduction based on system balancing

Authors

Tobias Breiten, Riccardo Morandin, Philipp Schulze

Abstract

We study linear quadratic Gaussian (LQG) control design for linear port-Hamiltonian systems. To this end, we exploit the freedom in choosing the weighting matrices and propose a specific choice which leads to an LQG controller which is port-Hamiltonian and, thus, in particular stable and passive. Furthermore, we construct a reduced-order controller via balancing and subsequent truncation. This approach is closely related to classical LQG balanced truncation and shares a similar a priori error bound with respect to the gap metric. By exploiting the non-uniqueness of the Hamiltonian, we are able to determine an optimal pH representation of the full-order system in the sense that the error bound is minimized. In addition, we discuss consequences for pH-preserving balanced truncation model reduction which results in two different classical H ∞ -error bounds. Finally, we illustrate the theoretical findings by means of two numerical examples.

Keywords

error bounds, lqg control design, model order reduction, port-hamiltonian systems

Citation

• Journal: Computers & Mathematics with Applications
• Year: 2022
• Volume: 116
• Issue:
• Pages: 100–115
• Publisher: Elsevier BV
• DOI: 10.1016/j.camwa.2021.07.022
• Note: New trends in Computational Methods for PDEs

BibTeX

@article{Breiten_2022,
  title={{Error bounds for port-Hamiltonian model and controller reduction based on system balancing}},
  volume={116},
  ISSN={0898-1221},
  DOI={10.1016/j.camwa.2021.07.022},
  journal={Computers \& Mathematics with Applications},
  publisher={Elsevier BV},
  author={Breiten, Tobias and Morandin, Riccardo and Schulze, Philipp},
  year={2022},
  pages={100--115}
}

Download the bib file

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