Models of Production Systems taking into Account Uncertainties and Disturbances

The study is devoted to the development and research of new models and methods for the analysis and synthesis of the management of modern integrated facilities – "production, retail, recycling", which are in active stochastic environment of suppliers, competitors, consumers. The analysis of analogues and prototypes revealed factors that guarantee the failure of new research and developments: – based only on Gaussian statistics, simplified models of object dynamics, search methods of large systems optimization. The classification of sources and "generating mechanisms" of the disturbances is carried out, models of nonlinear transformations of stochastic processes are presented. The paper presents the formulation and solution of problems of analyzing the influence of uncertainties and disturbances based on: – building of the resource simulation models of objects – "virtual reality statistics generators"; – using the optimal aggregation methodology to calculate the optimal operational and strategic management in the simulation model. The problems of obtaining probability distributions for non-linear transformations, in particular for the "cost, output" functions, are set and solved. Examples of the analysis of hyperbolic rank distributions and multimodal income probability distributions for the producer systems of a certain production segment are given. The development results made it possible to substantiate the conclusion about essentially non-Gaussian statistics of modern production systems and the recommendation about the need to study the statistics of optimal adaptive developing systems.