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.