ON SOME ROBUSTNESS ISSUES IN INPUT DESIGN

Abstract

It is commonly believed that solutions to optimal input design problems for identification of dynamical systems often are sensitive to the underlying assumptions. For example, a wide class of problems can be solved with sinusoidal inputs with the same number of excitation frequencies (over the frequency range (–π, π]) as number of estimated parameters. With such an input it is not possible to check whether the true system is of higher order or not since then the input is not persistently exciting enough. In this contribution we argue that the optimal solution is often not unique and that there are alternatives to sinusoidal inputs which are more robust. For simplicity, we restrict attention to finite impulse-response models. For such a model of order n, it is only the n first auto-correlation coefficients of the input which determine the accuracy of the parameter estimate. Thus, the remaining coefficients can be used to make the solution more robust. For the problem of estimating some scalar system quantity J with a prescribed accuracy using minimum input energy, there is, under certain assumptions, an input spectrum that is optimal regardless of the model order. Furthermore, we show that using this input allows J to be estimated consistently even when the model order is lower than the true system order.