Stratified model of production management system

The production process control system is complex, so it is necessary to study it in advance on a model and select a multi-level structure for this purpose. Multi-level structures are divided into three classes: stratified, multi-layer and multi-echelon. The stratified model, on the one hand, allows to simplify the description and understanding of production control processes, reduce the multi-connectivity of control loops, on the other hand, it systematizes control tasks by strata and creates a basis for the application of rigorous mathematical tools. This is achieved by increasing the independence of strata and transferring their interrelation to output results. The paper shows that in the simplest case, using the superposition principle, the assessment of the control result can be reduced to the assessment of the result on the upper stratum. Identification of independently functioning parts of strata allows to organize the procedure of optimal redistribution of resources between them. The use of even simple models in the form of aperiodic links allows to formulate and solve the problem of optimal control at the level of each stratum, reducing it to solving a system of first-order differential equations. As a result, optimal phase trajectories of the strata movement and algorithms for supplying optimal control actions in time, expressed through exponentials, are determined.

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