A unified approach for neural network-like approximation of non-linear functionals

In this paper, we give a universal approach to approximation of non-linear functionals and so called myopic input-output maps by neural network-like architectures. Strong theorems on equi-uniform approximation to functionals in abstract spaces are given. As applications, theorems on identification of non-linear systems, whose inputs belong to compact sets in C(R-q, R-p), are given. It is pointed out that: (1) the weighted approximation can be reduced to non-weighted approximation; (2) the continuous case and discrete case can be dealt with universally. (C) 1998 Elsevier Science Ltd. All rights reserved.