Models of Functional Dependencies of Elements in Sequences for Solving Problems of Control and Management

In paper developed version of the basic concepts, models and methods for the formulation and solution of problems of control and diagnosing of processes in systems, tasks of constructing models of processes in which the causal relationships of events are transformed into functional dependencies between elements in sequences, problems of formalizing of process control rules, etc. For this extended classical recurrent definition of the sequences, which presents the functional elements depending on the immediately preceding to them m elements to offered Z-recurrent definition, which defines the functional relationship between sets of elements in the sequence. The orders of Z-recurrent forms have the form of a set of numbers and are convenient for accurate and complete characterization of the connections of events in processes. The tasks of control, diagnosing, constructing new models of processes, assessing the complexity of processes and rules for managing processes can be formulated and solved using numerical indicators of Z-recurrent definitions. A classification of Z-recurrent definitions of sequences and a classification of processes are constructed, an algorithm for checking the feasibility of determining a Z-recurrent form for given sequences of form is developed. The Z-recurrent definition of sequence is complemented by the Z-recurrent sequence pattern method, which includes: introducing a linear order on the base set of sequence elements, constructing an image for the sequence in the form of a sequence of executing or non-executing relationships between the elements represented by a linear order, and applying Z-recurrent definitions to the constructed image of the sequence. The problem on which the solution of the considered problems is based is the recognition of two sequences by properties, which are determined by the indicators of Z-recurrent definitions of sequences, which have the form of orders of Z-recurrent forms. Sets of orders in executing or non-executing Z-recurrent forms characterize the sequences and the analyzed sets of sequences, which allows you to set and solve problems related to system management: problems of control and diagnosing of processes in the system, problems of constructing process models, problems of formalizing and complexity estimation of control rules of processes.