#### Occupation Kernels and Densely Defined Liouville Operators for System Identification

#### Joel A. Rosenfeld; Rushikesh Kamalapurkar; Benjamin Russo; Taylor T. Johnson

#### 2019 IEEE 58th Conference on Decision and Control (CDC)

This manuscript introduces the concept of Liouville operators and occupation kernels over reproducing kernel Hilbert spaces (RKHSs). The combination of these two concepts allow for the embedding of a dynamical system into a RKHS, where function theoretic tools may be leveraged for the examination of such systems. These tools are then turned toward the problem of system identification where an inner product formula is developed to provide constraints on the parameters in a system identification setting. This system identification routine is validated through several numerical experiments, where each experiment examines various contributions to the parameter identification error via numerical integration methods and parameters for the kernel functions themselves.