This scientific work aims to represent some elements of the theory of identification that are important for both practical use and further theoretical research in order to build logically complete basic and applied theory of identification as mathematically reasonable theory of knowledge of the cause-and-effect relationship in the objects of the real world. For those specialists who carry out theoretical and experimental researches (technical, economic, biological, social etc) of the real-world objects with the aim of their optimal adaptive control, diagnostics of state, forecasting the consequences and so on. It will be useful for students, postgraduates and doctoral research scholars who study the real objects.
