Nonlinear system identification with limited time data

With disturbances modeled by arbitrary solutions to a linear homogeneous differential equation, a least squares-equation error method is developed for parameter identification using data over a limited time interval which has application to certain classes of nonlinear and time varying systems. Examples include the Duffing, Hammerstein, Mathieu and Van der Pol equations together with a class of bilinear systems. The technique seeks to determine the parameters characterizing the disturbance modes in addition to the system parameters, based on the input-output data collected over the finite time interval. The approach circumvents the need to estimate unknown initial conditions through the use of a certain projection operator. Computational considerations are discussed and simulation results are summarized for the Van der Pol equation.