SOME REMARKS ON ADAPTIVE NEURO-FUZZY SYSTEMS

Abstract

In this brief note we make three remarks concerning adaptive implementations of neural networks and fuzzy systems. First, we bring to the readers attention the fact that the potential power of these systems as function approximators is lost when, as in some recently published works, the adjustable parameters are only the linear combination weights of the basis functions. Second, we show that the stability analysis in those papers in any way uses properties particular to neural nets or fuzzy systems and follows immediately from well-established results in adaptive systems theory. The second fact is well known to people familiar with adaptive systems theory, but not necessarily so to the neuro-fuzzy community. On the other hand, the opposite seems to be the case for the first remark. Finally, we present a simple version of a result on adaptive stablilization of non-linearly parametrized non-linear systems which might be useful for the stability analysis of adaptive neuro-fuzzy systems. This result, though well known in the Russian literature for a long time, has apparantly been overlooked in ‘western’ publications.