On finding ´exciting´ trajectories for identification experiments involving systems with non-linear dynamics

When designing an identification experiment for a system described by non-linear functions, such as those of manipulator dynamics, it is necessary to consider the sufficiency of excitation. It is shown that the convergence rate and noise immunity of a parameter identification experiment depend directly upon the condition number of the persistent excitation matrix. A method is presented to optimize this condition number using the calculus of variations. Analysis of condition numbers of several trajectories has shown that intuitively selected trajectories can be very poorly conditioned. The optimizer applied to the best trajectory in one experiment reported in the literature has reduced the convergence time from 1 hour and 25 minutes to 4 minutes.