Approximation of Time-Varying Functions with Local Regression Models

Abstract

Industrial or robot control applications which have to cope with changing environments require adaptive models. The standard procedure of training a neural network off-line with no further learning during the actual operation of the network is not sufficient in those cases. Therefore, we are concerned with developing algorithms for approximating time-varying functions. We assume that the data arrives sequentially and we require an immediate update of the approximating function. The algorithm presented in this paper uses local linear regression models with adaptive kernel functions describing the validity region of a local model. While the method is developed to approximate a time-variant function, naturally it can also be used to improve the fit for a time-invariant function. An example is used to demonstrate the learning capabilities of the algorithm.