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

TL;DR

This paper introduces a gradient-based, structure-preserving algorithm for identifying system matrices of linear port-Hamiltonian systems from time domain input-output data, ensuring stability and physical properties are maintained.

Contribution

It develops a novel direct structure-preserving optimization method for port-Hamiltonian systems that guarantees stability and matrix properties during identification.

Findings

Method successfully identifies system matrices with synthetic data.

Preserves skew-symmetry and positive semi-definiteness during optimization.

Demonstrates effectiveness on benchmark and perturbed data.

Abstract

We present a gradient-based identification 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 demonstrate the feasibility of the approach.