Approximators characteristics and their effect on trainingmisbehavior in passive learning control

摘要

This paper investigates function approximator selection fornonlinear system identification under passive learning conditions.Passive learning refers to the normal situation in which the systeminputs cannot be selected freely by the learning system; instead,function approximation must be accomplished using the input/outputsamples obtained while the plant is in useful operation. Under theseconditions, the experimental sample density is not expected to beuniform over the learning domain. This is especially true over shortduration windows, where the training samples will cluster in subregionsof the learning domain. The effect of the nonuniform sample density onthe resulting parameter estimate has been previously analyzed. It hasbeen shown that approximators that have basis elements satisfyingcertain local support conditions can effectively accommodate nonuniformtraining sample distributions. Although such approximators require largeamounts of memory, parameter estimation algorithms can be implementedefficiently (i.e. the number of computations on the order of thatrequired for a linear adaptive controller for a problem of the samestate dimension) in real-time. This paper addresses the effect of localbasis elements on training behavior. The article shows that trackingerror, the means most often used to demonstrate performance, is not asuitable metric for measuring the learning system performance.Alternative performance measures are suggested. Examples are included