A continuous-time global adaptive observer of the parameters of a SISO sigmoidal neural network

A class of single-input single-output sigmoidal neural networks with nonlinear parametrization is considered. The problem of the continuous-time global exponential estimation of its parameters, both linearly and nonlinearly parametrized, is addressed. Under regularity assumptions on the neural network input trajectory, a novel solution to this problem is presented when the output, the input, and the input's derivative are available for measurement. The result is obtained showing that the sigmoidal neural network output coincides with the output of a suitable autonomous system of differential equations whose state and unknown parameters can be estimated with the tools of adaptive observation theory. If the sigmoidal neural network is the approximation of an arbitrary nonlinear mapping, the parameters estimates convergence is shown to be robust with respect to the neural network output approximation error.