Zeroing Neural Networks for Unknown Functions

The main goal of this paper is to propose new classes of zeroing neural networks that allow one to determine the zeros of an unknown function. This objective is pursued by using, both linear-in-parameters and nonlinear-in-parameters, adaptive schemes to estimate the function to be zeroed and a modified version of the Newton method to estimate a zero of the approximated function. If the function to be zeroed is known in parametric form, then the proposed method estimates one of its zeros exponentially fast, whereas if it is completely unknown, then the approximation error can be made arbitrarily small by using a sufficiently good approximation function.