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We present a gradient-based identification algorithm to identify the systemmatrices of a linear port-Hamiltonian system from given input-output time data.Aiming for a direct structure-preserving approach, we employ techniques fromoptimal control with ordinary differential equations and define a constrainedoptimization problem. The input-to-state stability is discussed which is thekey step towards the existence of optimal controls. Further, we derive thefirst-order optimality system taking into account the port-Hamiltonianstructure. Indeed, the proposed method preserves the skew-symmetry and positive(semi)-definiteness of the system matrices throughout the optimizationiterations. Numerical results with perturbed and unperturbed synthetic data, aswell as an example from the PHS benchmark collection demonstrate thefeasibility of the approach.

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