On the identifiability of nonlinear maps in a general interconnected system

We investigate the problem of identifying static nonlinear maps as part of a general, structured interconnected system. The static nonlinear maps that require identification are not naturally parameterized via basis functions or other expansions. Thus, we are interested in non-parametric identification of these nonlinear maps. The particular focus of the paper is the issue of “identifiability”. Loosely speaking, the static nonlinear maps in an interconnected system are identifiable if it is possible to determine them uniquely on the basis of input-output experiments. As is well known, identifiability concepts are of fundamental importance in system identification. We focus on the case where only the static nonlinearity needs to be identified and the linear components of the interconnection are known. We offer a readily computable test for identifiability in the case that the inputs to every nonlinear map are measured. This test reduces to a matrix positivity computation