Approximators characteristics and their effect on training misbehavior in passive learning control

This paper investigates function approximator selection for nonlinear system identification under passive learning conditions. Passive learning refers to the normal situation in which the system inputs cannot be selected freely by the learning system; instead, function approximation must be accomplished using the input/output samples obtained while the plant is in useful operation. Under these conditions, the experimental sample density is not expected to be uniform over the learning domain. This is especially true over short duration windows, where the training samples will cluster in subregions of the learning domain. The effect of the nonuniform sample density on the resulting parameter estimate has been previously analyzed. It has been shown that approximators that have basis elements satisfying certain local support conditions can effectively accommodate nonuniform training sample distributions. Although such approximators require large amounts of memory, parameter estimation algorithms can be implemented efficiently (i.e. the number of computations on the order of that required for a linear adaptive controller for a problem of the same state dimension) in real-time. This paper addresses the effect of local basis elements on training behavior. The article shows that tracking error, the means most often used to demonstrate performance, is not a suitable metric for measuring the learning system performance. Alternative performance measures are suggested. Examples are included