Recurrent approximation as the tool for expansion of functions and modes of operation of neural network

Abstract

The paper considers the role of recurrent artificial neural network (RANN) for the solution of specific problems of coordination control, the relevance of which is predetermined by the development of modern automated systems. We synthesized the RANN information processing structure that is formed based on the indicators - vectors and recurrent approximation of continuous function. New modes of its work and expanded functionality were examined. It was demonstrated that it is capable to implement zero correction modes, calibration, preparing information on the error of approximation, to solve the problem of minimization and act as a module of decision making support system. We proposed generalized algorithm for analytical determination of synaptic weights coefficients and evaluation of their error. It is shown that the application of the indicator vectors makes these algorithms practically independent of selecting initial approximation of synaptic weights coefficients, while the network acquires mechanism of readjustment during optimal control. For its implementation, depending on the changes that occur to the object, in accordance with the obtained analytical criteria of evaluation of error of synaptic weights coefficients, their readjustment is conducted. The synthesized structure is able to realize algorithms that provide a necessary set of operating modes and formation of productive or controlling rules based on the analysis of behavior of the set of the indicator vectors. Its structure forms the information support of the conditional part of the rules condition–action and implements effective part in the algorithms of coordination control. It also is capable to implement simple algorithms for finding roots and control that minimizes or maximizes continuous function or the Lagrange function under conditions of existence of restrictions of inequalities for a nonlinear object. The application of the obtained results is also useful for solving various separate problems: formation of productive rules for solving the problems of finding simple root of monotonic function, finding a not simple root of monotonic function, finding a root of oscillating function, selecting controlling influence and the problem on the synthesis of controlling influence. Obtained results continue and complement practical implementation of the idea of recurrent approximation for solving the tasks of modeling and design.