MATHEMATICAL MODELING OF CONTROL OF A DYNAMIC NEURAL NETWORK WITH DELAY

Currently, the world is actively developing a new applied area of mathematics, related to the study of artificial neural networks. Interest in them is caused both by theoretical and applied achievements: the possibilities of using computations in spheres previously related only to the field of human intelligence were opened. The relevance of research in this direction is confirmed by numerous examples of the use of neural networks in automation systems [1], robotics of image recognition processes [2], adaptive control [3], forecasting and creating expert systems [4], research of associative memory [5], etc. In complex practical tasks, the trained neural network acts as an expert. An example is medical diagnostics, where a neural network can take into account a large number of numerical parameters (electrical impulses of the nerve cells of the brain and its parts, recorded by means of encephalograms, pressure, weight, etc.). The aim of the work is to construct an artificial oscillatory neural network that can be used to model the activity of the brain: associative memory and attention. The model is formalized as a multicriteria optimal control problem with delay. The purpose of neural network management is its training, which includes the construction of an optimal process that meets the specified criteria. One of the criteria is the terminal criterion determining the state of the neural network at the final moment of time. The optimality conditions in the continuous model are obtained with the help of the Maximum principle for problems with delayed argument [6], [7], [8]. The boundary value problem of the maximum principle is constructed [9]. To obtain optimal conditions in a discrete model that approximates a continuous model, the method of rapid automatic differentiation and numerical methods for solving extremal problems are used [9], [10], [11]. The results of a numerical experiment are presented.

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