Functional series identification of nonlinear systems for adaptive control

The well-known techniques for nonlinear systems identification via Wiener or Cameron-Martin series expansion require Gaussian white noise (or, in certain variations, shot noise or broad band Gaussian noise) as a test input signal. Certain applications to adaptive control require the extension of these methods to cover inputs consisting of zero mean white noise superimposed on a deterministic reference signal. An extension of the Cameron-Martin expansion is made to cover this case, and the properties of this expansion (best representation theorem, Bessel inequality, mean square convergence, Parseval's theorem) are shown. An identification method based on a least-squares solution for the parameters of this expansion has been successfully tested in a computer simulation.