The methods of the control stochastic systems (CStS) research based on the parametrization of the distributions permit to design practically simple software tools. These methods give the rapid increase of the number of equations for the moments, the semiinvariants, coefficients of the truncated orthogonal expansions of the state vector Y, and the maximal order of the moments involved. For structural parametrization of the probability (normalized and nonnormalized) densities, we shall apply the ellipsoidal densities. A normal distribution has an ellipsoidal structure. The distinctive characteristics of such distributions consist in the fact that their densities are the functions of positively determined quadratic form of the centered state vector. Ellipsoidal approximation method (EAM) cardinally reduces the number of parameters. For ellipsoidal linearization method (ELM), the number of equations coincides with normal approximation method (NAM). The development of EAM (ELM) for CStS analysis and CStS filtering are considered. Based on nonnormalized densities, new types of filters are designed. The theory of ellipsoidal Pugachev conditionally optimal control is presented. Basic applications are considered.

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The development of tools for solving research problems with the use of domestic software and hardware is an urgent direction. Such tasks include the tasks of neural network modeling of nonlinear controlled systems. The paper provides an extended analysis of the capabilities of the Elbrus architecture and the blocks of the built-in EML library for mathematical modeling of nonlinear systems. A comparative analysis of the instrumentation and efficiency of computational experiments is performed, taking into account the use of an 8-core processor and the potential capabilities of a 16-core processor. The specifics of the EML library blocks in relation to solving specific types of scientific problems is considered and the optimized software is analyzed. The design of generalized models of nonlinear systems with switching is proposed. For generalized models, a new switching algorithm has been developed that can be adapted to the Elbrus computing platform. An algorithmic tree is constructed, and algorithmic and software are developed for the study of models with switching. The results of adaptation of the modules of the software package for modeling managed systems to the elements of the platform are presented. The results of computer modeling of nonlinear systems based on the Elbrus 801-RS computing platform are systematized and generalized. The results can be used in problems of creating algorithmic and software for solving research modeling problems, in problems of synthesis and analysis of models of controlled technical systems with switching modes of operation, as well as in problems of neural network modeling and machine learning.

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