Study of Dynamic Processes in Nonlinear Discrete Systems with Delay Based on Graph Models

In connection with the problems of development and implementation of perfect automatic and automated control systems for complex technological processes based on modern information technology tools, the development of research methods for multidimensional nonlinear discrete control systems is of particular relevance. The variety of these systems is due to the types of modulation, non-linearities, modes of operation of impulse elements, characteristics of continuous parts. The article deals with the problems of modeling and research of one-dimensional and multidimensional pulse-frequency systems with delay based on the use of dynamic graphs. One of the key points in solving the problem is an approach based on the maximum consideration of the physical features of these systems. Given the structural complexity of systems, it is necessary first of all to establish the possibility of decomposing the system into simpler subsystems. Then the study of the system can be reduced to the study of individual subsystems and the nature of their interaction, that is, to the determination of the properties of the system as a whole by the properties of its elements. Systems with frequency-pulse modulation are essentially non-linear systems. The topological method based on dynamic graph models allows solving the fundamental difficulties of studying nonlinear discrete systems with delay, allows clearly and strictly formalizing their description, and makes it possible to obtain effective algorithms for analyzing one-dimensional and multidimensional systems of this class. The article presents an example of using the obtained algorithm.