Abstract: The object of research in this work are the control systems of complex technical complexes. The subject of research is the methodology for developing control systems for complex technical complexes. The developed methodology for creating a control system for complex technical complexes is based on the idea of generating a sequence of mappings of conceptual models into infological models and, further, into datalogical models. Previously, the author presented conceptual and infological modeling and the mathematical models corresponding to these levels, as well as the relations between them, that is, mathematical categories. The developed methodology for creating a control system for complex technical complexes is based on the methods of the theory of mathematical categories. The categories presented in the datalogical representation have two levels of abstraction. The main findings of the study:1. A unified description of families of inhomogeneous mathematical models reflecting a different level of abstraction (generalization) at the stage of the datalogical presentation of subject problems makes it possible to create formulations for the general definition of models with a description of their structure.2. The developed method of datalogical modeling provides all the possibilities for providing customization on specific software and hardware tools for implementing a control system for complex technical complexes.

Abstract: This article is devoted to the the methods used in the theory of Ñomputer-Assisted Design. Development of a theoretical framework of technologies of the automated designing is an important scientific problem. One of directions employed to solve this problem is its reduction to a single universal formalism used for describing a variety of technologies, which will be appropriate for the design of complex heterogeneous systems for integration and coordination of these technologies. The solution to this problem depends on the choice of the mathematical apparatus. In this article the author proposes creation of the computer-aided design methods using mathematical category theory. The author then discusses methods for the formation of a mathematical apparatus for CAD based on the mathematical category theory in order to establish mathematical models and the correlations between them at different levels of abstraction. It is shown that the formulation of regularities in the mapping from conceptual view the conceptual view of the subject objectives the basic reasons are: a consistent mathematical apparatus of formation models;  an uniform structure of the regularities of formation models; existence of the laws of cyclicality. Pattern display models of conceptual representation in the model conceptual representation of the subject is the identity in the application of functional abstractions for dynamic and static components during the process of formation (establishment) of the relations between them and the identity of the models on the same level of abstraction with the same view.