Parameter identification for a class of polynomial differential systems

A least squares parameter identification technique is developed for a class of nonlinear deterministic 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 sequential time intervals, the underlying computations utilize a Fast Fourier Transform algorithm on polynomials of the data without the need for estimating unknown initial conditions at the start of each finite time interval.