  Many engineered as well as naturally occurring dynamical systems do not have
an accurate mathematical model to describe their dynamic behavior. However, in
many applications, it is possible to probe the system with external inputs and
measure the process variables, resulting in abundant data repositories. Using
the time-series data to infer a mathematical model that describes the
underlying dynamical process is an important and challenging problem. In this
work, we propose a model reconstruction procedure for inferring the dynamics of
a class of nonlinear systems governed by an input affine structure. In
particular, we propose a data generation and learning strategy to decouple the
reconstruction problem associated with the drift- and control- vector fields,
and enable quantification of their respective contributions to the dynamics of
the system. This learning procedure leads to an interpretable and reliable
model inference approach. We present several numerical examples to demonstrate
the efficacy and flexibility of the proposed method.

Optimization and Control