Conceptual foundations of general theory of discrete dynamic, relay and logical-dynamic systems based on physical decomposition and graph models

Among many different types of automatic control systems, discrete dynamic and logical-dynamic control systems are of greatest theoretical and practical interest. This is explained by a wide demand for these systems in the industry, aviation, aerospace, radiolocation, defense industry and other fields. At the same time, the modern theory of automatic control has enough effective methods of calculation and design for linear systems. The results obtained for non-linear and logical-dynamic systems are usually of a private nature and belong to a class of non-linearities or logical devices. In this connection, an important issue is the formation of a general theory of discrete dynamic and logical-dynamic control systems. The analysis of discrete dynamical, relay and logical-dynamic systems shows the presence of factors of complexity inherent in each of the subclasses (types, kinds) of these systems. First of all, the structural complexity of managed objects, the combination of logical and dynamic variables and conditions, the variability of the structures and parameters, modes of operation of the pulse elements, nonlinear kinds of modulations, delay, etc. The difficulties arise in comprehensive manifestation of systems in all or several of these factors. However, this is characteristic of a complex system of automatic control. The article presents the conceptual foundations of the general theory of discrete dynamical and logical-dynamic systems on the basis of shared fundamental properties of these classes - discrete structures and physical decomposition.