Abstract. We consider the problem of training of neural networks and neural-fuzzy systems, leading to separable models structures nonlinear in some unknown parameters and linear in the others. New algorithms for their training are proposed, based on the nonlinear optimization problem that includes a priori information only on nonlinear input parameters. It is assumed that it can be obtained on a training set, the distribution of the generating set or linguistic information. To solve the problem, the Gauss–Newton method with linearization in the vicinity of the last estimate, asymptotic representations of the pseudo-inverse of perturbed matrices, and separable structure of the models are used. The obtained algorithms have several important properties: they do not require selection of initial values of the linear parameters, which may lead to divergence, but at the same time it is not necessary to find the partial derivatives of the projection matrix; they can be used in serial mode and batch processing; as a special case, well-known algorithms follow from them, and the simulation shows that the proposed algorithms can surpass them in accuracy and rate of convergence.

Keywords: separable regression, neural network, neuro-fuzzy system, learning algorithm.