Dynamic Networks: Representations, Abstractions, and Well-Posedness

This paper introduces notions of abstraction and realization for dynamic networks. These processes generate dynamically equivalent representations of a system, but with varying degrees of structural detail. Nuanced definitions and associated conditions for maintaining well-posedness for these multi-resolution representations of a dynamic system are then detailed, ensuring that hierarchies of network representations are sensible as multi-resolution models of dynamic networks. Although the ideas are developed precisely here for LTI networks, many of the concepts remain fundamental in the nonlinear setting.