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Differentiation of nonlinear transformations of artificial neural how implicit functions


V.V. Vasetsky – Ph. D. (Eng.), Associate Professor, Russian Air Force Military Educational and Scientific Center «Zhukovsky–Gagarin Air Force Academy» (Voronezh). E-mail:

One of the most suitable methods for the intellectualization of existing automated control systems is the use of artificial neural networks, which have properties similar to those of the human brain, such as associative generalization, parallel search, adaptation to environmental changes. Artificial neural network is a collection of neuron-like elements in a certain way connected with each other and with the environment through connections defined weight coefficients. Artificial neuron (ID) is part of the INS. It consists of three types of elements: multipliers ( synapses ), adder and nonlinear transformations of users. Synapses helps communication between IN, multiplies the input signal by the characterizing the binding force (weight of the synapse) number. The adder adds the signals received by the synaptic connections of other artificial neurons to external input signals. Nonlinear converter implements a nonlinear function of one argument – the output of adder. This function is called the activation function or the transfer function of ID. Using the method of differentiation of the implicit function for the nonlinear converter artificial neuron will expand the number of types of transfer functions and simplify the training of neural networks used in automatic control systems.

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