Learnability of Linear Port-Hamiltonian Systems

A complete structure-preserving learning scheme for single-input/single-output (SISO) linear port-Hamiltonian systems is proposed. The construction is based on the solution, when possible, of the unique identification problem for these systems, in ways that reveal fundamental relationships between classical notions in control theory and crucial properties in the machine learning context, like structure-preservation and expressive power. In the canonical case, it is shown that, {up to initializations,} the set of uniquely identified systems can be explicitly characterized as a smooth manifold …

construction context control identification linear machine machine learning power preservation relationships solution systems theory