$Z$-recurrent process structures in problems of control and diagnostics

The main provisions, models and methods for solving the problems of control and diagnosing of processes in the system by the indicators of changes in the relationships of events in processes are developed. For this, for the first time the classical recursive definition of sequences is extended to $Z$-recurrent definition of sequences, which allows to represent processes by formal models in the form of orders of $Z$-recurrent forms. A classification of the orders of $Z$-recurrent forms and algorithms for solving the problems of control and diagnosing processes to a system using the representation of processes by the orders of $Z$-recurrent forms are developed. To increase the efficiency of calculating the orders of $Z$-recurrent forms, an algebra of the precedence relations of elements has been developed, the formulas of which allow one to develop methods for calculating the orders of $Z$-recurrent forms.