2023/09/11 by Tobias Holicki, Holicki, Tobias, Jonas Nicodemus +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Engineering · #37J06 #37M99 #65P10 #90C22 #93A30 #93C05 #ATP Synthase and ATPases Research #Advanced Control Systems Optimization #Dynamical Systems (math.DS) #FOS: Mathematics #Fuel Cells and Related Materials #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2309.05778
openalex publication_date 2023/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well known that any port-Hamiltonian (pH) system is passive, and conversely, any minimal and stable passive system has a pH representation. Nevertheless, this equivalence is only concerned with the input-output mapping but not with the Hamiltonian itself. Thus, we propose to view a pH system either as an enlarged dynamical system with the Hamiltonian as additional output or as two dynamical systems with the input-output and the Hamiltonian dynamic. Our first main result is a structure-preserving Kalman-like decomposition of the enlarged pH system that separates the controllable and zero-state observable parts. Moreover, for further approximations in the context of structure-preserving model-order reduction (MOR), we propose to search for a Hamiltonian in the reduced pH system that minimizes the H2-distance to the full-order Hamiltonian without altering the input-output dynamic, thus discussing a particular aspect of the corresponding multi-objective minimization problem corresponding to H2-optimal MOR for pH systems. We show that this optimization problem is uniquely solvable, can be recast as a standard semidefinite program, and present two numerical approaches for solving it. The results are illustrated with three academic examples.