Least squares parameter identification of nonlinear differential I/O models

A least-squares parameter identification technique is formulated for deterministic systems modeled by a class of input-output nonlinear differential operator equations. Based on the notion of exactness in the calculus, a distinction is made on the basis of whether or not the equation error representation is an exact differential expression. It is shown how equation error models which are exact can be integrated for any given input-output data pair to yield and explicit function of the parameters that can be used for standard least-squares-estimation techniques. The formulation is then extended to apply to a class of inexact equation error system models. Also discussed is the notion of `identifiability´ as it relates to the class of systems under consideration