  Markov chain-based modeling and Koopman operator-based modeling are two
popular frameworks for data-driven modeling of dynamical systems. They share
notable similarities from a computational and practitioner's perspective,
especially for modeling autonomous systems. The first part of this paper aims
to elucidate these similarities. For modeling systems with control inputs, the
models produced by the two approaches differ. The second part of this paper
introduces these models and their corresponding control design methods. We
illustrate the two approaches and compare them in terms of model accuracy and
computational efficiency for both autonomous and controlled systems in
numerical examples.
