A new approach and methods of mathematical modeling of technical objects belonging to the class of objects with discrete-distributed parameters in time or space are considered. The main purpose of the proposed mathematical methods and approach - application in distributed automated control systems, forecasting and management to support the solution of problems of ensuring the economy and safety of objects . The proposed approach is based on the principles of structural and temporal decomposition of multidimensional processes in mathematical modeling, in particular. use of a customizable orthogonal basis, obtained during component decomposition of the Shura or singular decomposition of the scatter matrices by a sample of implementations of the process , use of pre-clustering of process implementations, the use of decomposition of the process by universal quasi-orthogonal basic functions - enveloping functions, and t. p. For scientists and specialists interested in the problems of modeling, recognition and forecasting of energy and other technological processes .