Disentangling Drift- and Control- Vector Fields for Interpretable Inference of Control-affine Systems

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.