System identification of distributed parameter system with recurrent trajectory via deterministic learning and interpolation

摘要

In the paper, we propose a novel approach to identify distributed parameter system (DPS) with recurrent state trajectory. Different from existing literature, the system dynamics rather than parameters or structure of DPS is identified in the study. Due to the infinite-dimensional feature of DPS, the partial differential equation describing the DPS is first approximated by a set of ordinary differential equations. By employing finite difference method, the spatial derivatives at a set of spatial points are approximated. Then, the DPS dynamics at the set of spatial points is identified via deterministic learning. With the identification results, a mechanism based on interpolation method is proposed to approximate the DPS dynamics at any other spatial point. That is, we can accurately identify the DPS dynamics at any spatial point. Numerical results involving the identification of an important mathematical physics equation are presented to illustrate the validity of the approach.