We exploit the key idea that nonlinear system
identification is equivalent to linear identification of the socalled
Koopman operator. Instead of considering nonlinear
system identification in the state space, we obtain a novel
linear identification technique by recasting the problem in the
infinite-dimensional space of observables. This technique can
be described in two main steps. In the first step, similar to
a component of the Extended Dynamic Mode Decomposition
algorithm, the data are lifted to the infinite-dimensional space
and used for linear identification of the Koopman operator. In
the second step, the obtained Koopman operator is “projected
back” to the finite-dimensional state space, and identified to the
nonlinear vector field through a linear least squares problem.
The proposed technique is efficient to recover (polynomial)
vector fields of different classes of systems, including unstable,
chaotic, and open systems. In addition, it is robust to noise,
well-suited to model low sampling rate datasets, and able to
infer network topology and dynamics
