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

• Published in: Programming and computer software Vol. 49; no. 2; pp. 108 - 121
• Main Authors: Demidova, A. V., Druzhinina, O. V., Masina, O. N., Petrov, A. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.04.2023; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Comparative analysis; Computer algebra; Computer Science; Control stability; Control theory; Differential equations; Dynamical systems; Equilibrium; Evolution; Global optimization; High level languages; Libraries; Mathematical analysis; Matrix algebra; Methods; Operating Systems; Optimization algorithms; Ordinary differential equations; Population; Programming languages; Python; Runge-Kutta method; Software; Software Engineering; Software Engineering/Programming and Operating Systems; Software packages; Software utilities; Stochastic models; Synthesis
• ISSN: 0361-7688; 1608-3261
• DOI: 10.1134/S036176882302007X

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.