The purpose of the work is to formalize the concepts and principles that form the basis of the mathematical model for controlling the life cycles of intelligent systems. The controlling elements formal description is part of a universal model of such systems. This model part is important for implementing complex intelligent systems with a large amount and diversity of knowledge flows and knowledge processing schemes performed simultaneously. The other two areas of this model are associated with a unified logical-algebraic description of the concept of knowledge representation formalism, as well as concepts related to the architecture of intelligent systems. Formalization of ideas about control in intelligent systems is carried out according to the principle of a hierarchy of controlling elements and processes. The elements of the mathematical model that implements this principle correspond to event-controlled automata with infinite memory and associated algorithms for the automata simulation in specific systems. The objectives of the research include the development of formats for describing the hierarchy of diagrams and assemblies of control elements in a universal model of an intelligent system, and diagrams of algorithms for the functioning of intelligent systems based on the processing of model descriptions. Models of intelligent system control elements hierarchy and execution algorithms for the sets of activated control elements for the implementation time of life cycles of intelligent systems are described by extending the special ontological structures. These structures implement customizations of universal control model