Fractional Order System Identification with Occupation Kernel Regression

Abstract

While fractional order systems have been employed broadly throughout science and engineering, system identification aimed at nonlinear fractional order dynamical systems remain in their infancy. One reason for this is that local estimates cannot be used to obtain a sample of fractional order dynamics in the same way that is done for integer order systems. This manuscript leverages occupation kernels to poise a trajectory as the fundamental unit of data from a fractional order dynamical system. When combined with a regularized regression problem, an approximation of fractional order dynamics is obtained as a linear combination of occupation kernels. A battery of numerical experiments are executed to validate the developed method, and it is demonstrated over two dynamical systems that accurate estimates of fractional order dynamics can be obtained both along trajectories and also nearby regions.