Identification of Stable Linear Systems Using Polynomial Kernels

Abstract

This paper deals with the identification of stable linear systems from input−output response data with low signal/noise ratios. Specifically we focus on nonparametric (finite impulse or step response, FIR or FSR) models widely used in model predictive control. A polynomial kernel representation is proposed to reduce the number of parameters needed to represent the model. This leads to parsimonious yet robust models. Linear least-squares estimation can be used with these polynomial models. The time delay and response time of the process can be explicitly included as parameters in the model; however, the nonlinear optimization method must then be used. Various properties of this model including the variance of parameter estimates are given in the paper. Both colored and white noise are considered. Simulation and experimental results are used to illustrate the advantages of this approach especially at low signal/noise ratios. The polynomials act as an adaptive filter to remove the noise.