The issues of processing bulk materials are of great importance in the energy, pharmacology, and chemical industries. New technologies have new requirements for the granulometric characteristics of individual components of powders and their mixtures. Often, the components of a mixture differ in their properties and grain sizes, thus, multi-stage processing of these mixtures is required to obtain powders with desired technological properties. Optimal control of the structure and operating modes of complex multi-stage apparatus to obtain powders with desired properties is a topical task. Methods of probability theory and fractional mass balance equations are used to model multistage gravitational classifiers. Mathematical programming methods are applied to solve optimization problems of powder classification. A generalized method of combinatorial matrix description of an open stage of regular multiproduct classifying elements for an arbitrary number of finished products is proposed. The proposed model of the considered stage is used for the matrix description of a closed system of devices with an arbitrary flow structure. The authors have determined the best structures and operating modes of individual stages to obtain powders with specified technological properties. The developed approach makes it possible to optimally control the structure of the cascade of classifiers and the modes of operation of its individual stages to obtain powders with desired technological properties, as well as to design systems for predictive diagnostics of the state of these installations in the energy, pharmacological and chemical industries.