AAS 95-338

The Source of the Often Observed Property of Initial Convergence Followed by Divergence in Learning and Repetitive Control

Y-C. Huang and R. W. Longman, Columbia University, New York, NY

Abstract

A previous paper by the authors detailed the used of unstable repetitive control laws for increased tracking accuracy. Repetitive control often exhibits the same property as asymptotic expansions, that the expansion in fact diverges, yet if one takes an appropriate number of terms in the expansion of a function, one gets a very good representation of the function. In simple repetitive control, the learning process can easily be unstable, but the tracking error decreases significantly in the early repetitions of the learning process before it starts to diverge. Thus, in practice it is often possible to obtain significant improvements over feedback control, by using the repetitive control signal associated with minimum error in a divergent learning process. It is the purpose of this paper to understand the source of this asymptotic expansion behavior, in order to be able to predict what problems will exhibit the behavior.