Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain

Authors

Michael Günther, Birgit Jacob, Claudia Totzeck

Abstract

We present a gradient-based calibration algorithm to identify the system matrices of a linear port-Hamiltonian system from given input–output time data. Aiming for a direct structure-preserving approach, we employ techniques from optimal control with ordinary differential equations and define a constrained optimization problem. The input-to-state stability is discussed which is the key step towards the existence of optimal controls. Further, we derive the first-order optimality system taking into account the port-Hamiltonian structure. Indeed, the proposed method preserves the skew symmetry and positive (semi)-definiteness of the system matrices throughout the optimization iterations. Numerical results with perturbed and unperturbed synthetic data, as well as an example from the PHS benchmark collection [ 17 ] demonstrate the feasibility of the approach.

Keywords

Port-Hamiltonian systems; Data-driven approach; Optimal control; Adjoint-based calibration; Time domain; Coupled dynamical systems; Structure preservation; 37J06; 37M99; 49J15; 49K15; 49M29; 49Q12; 65P10; 93A30; 93B30; 93C05

Citation

• Journal: Mathematics of Control, Signals, and Systems
• Year: 2024
• Volume: 36
• Issue: 4
• Pages: 957–977
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s00498-024-00389-2

BibTeX

@article{G_nther_2024,
  title={{Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain}},
  volume={36},
  ISSN={1435-568X},
  DOI={10.1007/s00498-024-00389-2},
  number={4},
  journal={Mathematics of Control, Signals, and Systems},
  publisher={Springer Science and Business Media LLC},
  author={Günther, Michael and Jacob, Birgit and Totzeck, Claudia},
  year={2024},
  pages={957--977}
}

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