Neural Network Estimation of the Dynamics of the Automatic Optimization System

Abstract

The topic of the article is a search engine for an automatic optimization of the nonlinear object of control with algorithm for search of the extremum of nonlinearity and storing of the extremum. The traditional methods of regulation realized on the basis of the theory of the linear and linearized systems cannot ensure the demanded quality of regulation of the technological parameters of many industrial facilities, which are inherently nonlinear. There is a need for solution to the traditional problems of control with the use of the new methods implemented in smart systems, in particular, the neural network methods. The aim of the work is to solve the problem of an approximate assessment of the transition processes with the use of a neural network of perseptronny type in coordinates, the exit time (z, t) of the control object, which gives a chance to construct an approximate assessment of the phase trajectory of the process in coordinates of the exit entrance (z, x) of the control object. For the solution of the problem of assessment of the dynamics of the exit of an object the neural network method is offered in the form of a three-layer network of perseptronny type with a function of activation of the sigmoidal type. Use of the sigmoidal function allows us to transfer from the binary exits of neurons to the analog ones. The unknown parameters of a network result from the solution of the nonlinear optimizing problem of a minimal total error. The signal of an error of the solution of a neural network is defined as a difference between the desirable and valid output signals in the discrete time points. Results of the computing experiment of calculation of the transition process of search for the extremum of nonlinearity by a neural network method show efficiency of the offered neural network method in comparison with the known numerical methods of the solution of the differential equations, differing in considerable simplicity and rather high precision due to the choice of the number of neurons in the hidden layer, and also considerable speed.