Identification of Nonlinear Maps in Interconnected Systems

We offer a systematic algorithm for the identification of static nonlinear maps in interconnected systems. The class of systems considered are those consisting of linear time-invariant systems and static nonlinear functions. Under the conditions that the linear dynamics are known and the inputs to the nonlinearities are measurable, the identification problem is reduced to a least squares problem. Notions of identifiability and persistence of excitation are introduced to demonstrate convergence of the estimate to the true nonlinear function under the L1-norm.