Identification of parametric dynamical systems using integer programming

Identification of nonlinear dynamical systems using data-driven frameworks facilitates the prediction and control of systems in a range of applications. Identification of a single system from the measurements of the system's states leads to the discovery of explicit or implicit models that cannot generalize beyond the system for which the data are provided. By learning the effect of parameters in the system, we propose a generalizable model for the Identification of Parametric forms of dynamical systems using Integer Programming (IP2). We first build general libraries of basis functions that take into account both states and parameters. Subsequently, leveraging dimension analysis and the assumption of having integer coefficients in the equations, we show that our framework can identify the exact forms of parametric mechanical dynamical systems like an ideal pendulum or an inverted pendulum on a cart. Moreover, by applying object tracking techniques and taking advantage of a sequential filtering scheme, we can identify the state and energy equations of these dynamical systems from videos of the systems, i.e. pixel space noisy data, rather than state-space measurements. The results show that using integer programming makes the proposed framework significantly (more than 40 times in the case of inverted pendulum on a cart) more robust to noise compared to previous optimization models.