Discrete-time Chen Series for Time Discretization and Machine Learning

A formal power series over a set of noncommuting indeterminants using iterated integrals as the coefficients is called a Chen series, named after the mathematician K.-T. Chen. The first goal of this paper is to give a brief overview of Chen series and their algebraic structures as a kind of reference point. The second goal is to describe its discrete-time analogue in detail and then apply the concept in two problems, the time discretization problem for nonlinear control systems and the machine learning problem for dynamical systems.