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Resistant training in radial basis function (RBF) networks is the topic of this paper. In this paper, one modification of Gauss-Newton training algorithm based on the theory of robust regression for dealing with outliers in the framework of function approximation, system identification and control is proposed. This modification combines the numerical ro- bustness of a particular class of non-quadratic estimators known as M-estimators in Statistics and dead-zone. The al- gorithms is tested on some examples, and the results show that the proposed algorithm not only eliminates the influence of the outliers but has better convergence rate then the standard Gauss-Newton algorithm

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519.71The problem of adaptive control over multidimensional nonlinear dynamic objects with the use of a neural network model is considered. To train the model, a recurrent least-squares method with exponential weighing of information and, to control an object, the multidimensional Kaczmarz algorithm are used. The results of an experimental investigation of the approach proposed are given.Introduction. The efficiency of control systems that are created to control real objects substantially depends on the quality of the mathematical models being used that, on the one hand, must most completely reflect the properties of the object being investigated and, on the other hand, must be convenient for realization of control algorithms. The absence of sufficiently complete information on the conditions of functioning, on the properties of the objects themselves, and on disturbances stipulate, during controlling objects, the necessity of using the adaptive approach that allows for simplified, in particular, linear models. Though this approach makes it possible to considerably reduce the a priori uncertainty and to realize a sufficiently efficient control in a number of cases, the use of only linear models not always provides the obtaining of the sought-for result. Therefore, the development of control systems based on the adaptive approach in combination with methods of the theory of artificial neural networks (ANNs) [1-3] seems to be more efficient.Based on this approach, a system of adaptive control is constructed whose structure is presented in Fig. 1.In solving the mentioned problems, multilayer perceptrons and radial-basis networks (RBF networks) have gained the most ground.The fact that both networks make it possible to approximate any continuous function with any preassigned accuracy ensured their wide application in problems of identification of nonlinear objects, and a combination of good approximating properties and the ability to be quickly trained allows one to use them for real-time control of nonlinear dynamic objects [3][4][5][6]. In both networks, the nonlinear operator of an object is approximated by some system of basis functions realized by neurons that form a layer of such a network, and the identification problem is reduced to the training of the corresponding network, i.e., to the adjustment of parameters of neurons on the basis of presentation of training pairs. Such training pairs are measurable values of the input and corresponding output variables.The training of a multilayer perceptron that contains several (mostly no more than two) hidden layers is usually realized with the help of an inverse error propagation algorithm whose realization faces substantial computational difficulties.The architecture of radial-basis networks is much simpler (they consist of one layer of neurons), and the use of efficient recurrent algorithms to train them determines the fact that these ANNs are preferred in solving identification and control problems in real time.Model of an object. Let us consider a multidimension...

Robust training of radial-basis networks under non-normally distributed noise is considered. The simulation results show that multistep projection training algorithms minimizing various forms of module criteria are rather efficient in this case.