PARAMETER-IDENTIFICATION IN THE PRESENCE OF NONPARAMETRIC DYNAMIC UNCERTAINTY

This paper provides identification laws which yield monotonic parameter error reduction in the absence of external noise inputs, but in the presence of non-parametric dynamic uncertainty (unmodelled dynamics). This paper considers two non-parametric uncertainty sets motivated by robust control: the weighted ball in H∞, and the weighted ball in the induced-L2 norm. The non-parametric uncertainty produces signals which corrupt the signals used in identification. This paper shows that the corruption is non-conservatively bounded in an L2 sense. This L2 bound is then compared with the signal energy, with the result used to enable/disable the parameter adjustment of a gradient least-squares adjustment mechanism. It is proved that the resulting parameter adjustment yields non-increasing parameter errors, with strictly decreasing parameter errors whenever the parameter errors are distinguishable from zero given the system input and output histories. © 1990.