On the identification of nonlinear maps in a general interconnected system

This paper is concerned with the problem of identifying static nonlinear maps in a general, structured interconnected system. These static nonlinear maps are nonparametric in that they do not have a natural parameterization that is known or suggested from an analytical understanding of the underlying process. Our technique involves selecting the nonlinear maps so as to maximize the “smoothness” or “staticness” of these maps while respecting the available input-output data and the noise model. These techniques avoid bias problems that arise when imposing artificial parameterizations on the nonlinearities. Computationally, these methods reduce to iterative least squares problems together with Kalman smoothing. Preliminary examples reveal the promise of these techniques