On optimal input design for nonlinear FIR-type systems

Abstract

We consider optimal input design for system identification of nonlinear FIR-type systems in the prediction error (PEM) framework. The input sequences are designed in terms of their statistical properties and not directly in time domain. The starting point is the asymptotic properties of PEM estimates. The fact that the inverse covariance matrix of the estimated parameters is linear in the input probability density function is exploited to formulate convex optimization problems. The main issues considered are the parameterization of the input pdf, reduction of the number of free variables in the optimization and to some extent signal generation. Two special model classes where tractable problems are obtainable are studied in detail. Convex formulations of the input design problem are presented for the static nonlinear and nonlinear FIR cases. Numerical examples of the discussed ideas are also presented.