Learning Parametric Dynamical Systems from Videos with Integer Programming

Identification of dynamical systems from measurements using data-driven frameworks enables us to model, predict, and control nonlinear systems. Existing explicit and implicit parsimonious models can discover the state equations of a single system provided the relatively clean measurements from sensors. These models, however, are usually limited to the observed system and depend significantly on the high quality of data that can be measured by expensive sensors. We propose a novel framework based on Integer Programming (IP) that can robustly identify the parametric forms of dynamical systems which generalize well to the other choices of parameters. Also, by processing the data using a sequential filtering scheme, the proposed model identifies some mechanical dynamical systems from visual inputs by transforming pixel-space videos into state-space data. We show that full equations of systems like an inverted pendulum on a cart can be identified robustly in the presence of artificial noise or noisy object trajectories extracted from videos.