On the effects of the training sample density 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 occur while the plant is in useful operation. Under these conditions, the experimental sample density is not expected to be uniform over the learning domain. The effect of the nonuniform sample density on the resulting parameter estimate is analyzed. It is shown that approximators that have orthonormal basis elements with local support can effectively accommodate nonuniform training sample distributions. Although such approximators require large amounts of memory, this paper shows that parameter estimation algorithms can be computed efficiently (i.e., on the order of the time required for a linear adaptive controller for a problem of the same state dimension) in real-time.