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Development of Algorithms and Software for Modeling Controlled Dynamic Systems Using Symbolic Computations and Stochastic Methods

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Abstract

The development of software for synthesizing and analyzing models of controlled systems taking into account their deterministic and stochastic description is an important direction of research. Results of the development of software for modeling dynamic systems the behavior of which can be described by one-step processes are presented. Models of population dynamics are considered as an example. The software uses a deterministic description of the model at its input to obtain a corresponding stochastic model in symbolic form and also analyze the model in detail (calculate trajectories in the deterministic and stochastic cases, find control functions, and visualize the results). An important aspect of the development is the use of computer algebra for analyzing the model and synthesizing controls. Methods and algorithms based on deterministic and stochastic Runge–Kutta methods, stability and control theory, methods for designing self-consistent stochastic models, numerical optimization algorithms, and artificial intelligence are implemented. The software was developed using high-level programming languages Python and Julia. As the basic tools, high-performance libraries for vector–matrix computations, symbolic computation libraries, libraries for the numerical solution of ordinary differential equations, and libraries of global optimization algorithms are used.

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Authors and Affiliations

  1. Peoples’ Friendship University of Russia (RUDN University), 117198, Moscow, Russia

    A. V. Demidova

  2. Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, 119333, Moscow, Russia

    O. V. Druzhinina

  3. Bunin Yelets State University, 399770, Yelets, Russia

    O. N. Masina & A. A. Petrov

Authors
  1. A. V. Demidova
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  2. O. V. Druzhinina
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  3. O. N. Masina
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  4. A. A. Petrov
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Corresponding authors

Correspondence to A. V. Demidova, O. V. Druzhinina, O. N. Masina or A. A. Petrov.

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The authors declare that they have no conflicts of interest.

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Translated by A. Klimontovich

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Demidova, A.V., Druzhinina, O.V., Masina, O.N. et al. Development of Algorithms and Software for Modeling Controlled Dynamic Systems Using Symbolic Computations and Stochastic Methods. Program Comput Soft 49, 108–121 (2023). https://doi.org/10.1134/S036176882302007X

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  • DOI: https://doi.org/10.1134/S036176882302007X

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