Control automata form an important part of control systems. A model of these automata that is widely used in the design process is the FSM (finite state machine), which is described by sets of inputs, outputs and states, an initial state and output and transition functions. It is shown that the use of classical FSMs for formalizing the properties of real systems leads to an increase in the dimensionality of the FSMs, which makes them more complex to understand and design. The objective of the study is to reduce the dimensionality of control automata models by expanding the functional capabilities of their elements. The research methodology involves revising and enhancing the properties of classical FSMs. The scientific novelty of the study lies in the systematization of existing and the development of new methods for reducing the dimensionality of graphic models of control automata and their formalization. To achieve this, the study introduces the use of controlled and non-binary au-tomata, differentiates output sets by isolating subsets of control parameters, and extends the structure of operational automata, as well as the output and transition functions of control automata that operate within a hierarchical system structure. As a result, set-theoretic models of control automata with enhanced functional capabilities have been developed. The practical value of the study is that the application of these proposed models allows reduction in the dimensionality of control automata used in complex systems.