On Finding Exciting Trajectories for Identification Experiments Involving Systems with Nonlinear Dynamics

Abstract

When designing an identification experiment for a system described by nonlinear functions such as those of manipulator dynamics, it is necessary to consider whether the excitation is sufficient to provide an accurate estimate of the parameters in the presence of experimental noise. It is shown that the convergence rate and noise immunity of a parameter identifi cation experiment depend directly on the condition number of the input correlation matrix, a measure of excitation. The sensitivity of an identification experiment to unmodeled dynamics is also studied; a dimensionless measure of this sensitivity—bias susceptibility—is proposed and related to excitation. The issue of how exciting a trajectory may be is addressed, and a method is presented to maximize the exci tation. Two identification experiments reported in the litera ture are studied; analysis of these experiments shows that intuitively selected trajectories may provide poor excitation, and considerable improvement results from employing the optimization to maximize excitation. A typical improvement is the reduction of parameter convergence time from 15 min to 33 s. This work illustrates the difficulty of maintaining persistent excitation during the experimental identification of complex models.