  We consider the problem of identifying a dissipative linear model of an
unknown nonlinear system that is known to be dissipative, from time domain
input-output data. We first learn an approximate linear model of the nonlinear
system using standard system identification techniques and then perturb the
system matrices of the linear model to enforce dissipativity, while closely
approximating the dynamical behavior of the nonlinear system. Further, we
provide an analytical relationship between the size of the perturbation and the
radius in which the dissipativity of the linear model guarantees local
dissipativity of the unknown nonlinear system. We demonstrate the application
of this identification technique to the problem of learning a dissipative model
of a microgrid with high penetration of variable renewable energy sources.
