On the identification of polynomial input-output differential systems

A least-squares parameter identification technique is formulated for a class of deterministic nonlinear systems modeled by polynomial input-output differential equations. The basis of the technique is Shinbrot´s method of moment functionals using trigonometric modulating functions. Given the input-output data over a single finite time interval for a one-shot estimate, or over a sequence of finite time intervals for sequential least squares, the underlying computations utilize a fast fourier transform algorithm on polynomials of the data without the need for estimating unknown initial or boundary conditions at the start of each finite time interval.