Koopman operator dynamical models: Learning, analysis and control

The Koopman operator allows for handling nonlinear systems through a globally linear representation. In general, the is infinite-dimensional – necessitating finite approximations which there no overarching framework. Although are principled ways of learning such approximations, they in many instances overlooked favor of, often ill-posed and unstructured methods. Also, theory has long-standing connections to known system-theoretic dynamical system notions that not universally recognized. Given former latter realities, this work aims bridge gap between various concepts regarding both tractable realizations. Firstly, we review data-driven representations (both structured) models, categorizing existing methodologies highlighting their differences. Furthermore, provide concise insight into paradigm’s relation analyze prospect using paradigm modeling control systems. Additionally, outline current challenges comment on future perspectives.