Some remarks on adaptive neuro-fuzzy systems

Makes three remarks concerning adaptive implementations of neural networks and fuzzy systems. First, the author brings to the readers attention the fact that the potential power of these systems as function approximators is lost when, as done in recently published work, the adjustable parameters are only the linear combination weights of the basis functions. Second, the author shows that the stability analysis in those papers 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, the author presents a simple version of a result on adaptive stabilization of nonlinearly parametrized nonlinear 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 apparently been overlooked in "western" publications.