To the issue of decomposition of mathematical models of disturbed motion of complex discrete-continuous dynamic systems

E. Aleksandrov, Tatyana Aleksandrova, Y. Morgun, M. Kholodov, O. Yaryta, V.А. Shapovalenko
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Abstract

Problem. Usually, complex dynamic systems are characterized by a high order of equations in their mathematical models and intricate interconnections among subsystems that constitute the complex dynamic system. Naturally, the analysis and synthesis of complex dynamic systems require the use of powerful computational systems with vast memory and high processing speed. Goal. The aim is quantitative assessment of the influence of the continuum part of a dynamic system on the behavior of its discrete part and the possibility to perform decomposition of the mathematical model of perturbed motion of a discrete-continuum system based on this assessment. Methodology. The measures are aimed at addressing issues that are based on the discrete-continuum capabilities and their decomposition. Results. For three types of complex dynamic systems described by infinite-dimensional systems of ordinary differential equations, quantitative assessments of the influence of the continuum part on the discrete part of the system have been proposed. These assessments determine the decomposition of the mathematical models of perturbed motion for such systems. Originality. Simplified mathematical models for three types of discrete-continuous dynamic systems were obtained. Practical value. The obtained results can be recommended for the study of the specialized course on the motion characteristics of cargo trucks during the transportation of liquids in tanks. Through optimization using the MATLAB software package, it is possible to simulate various parameters of both the cargo truck and the cargo being transported.
研究了复杂离散-连续动力系统扰动运动数学模型的分解问题
问题。通常,复杂动力系统的数学模型具有高阶方程,构成复杂动力系统的子系统之间具有复杂的相互联系。当然,复杂动态系统的分析和综合需要使用具有巨大内存和高处理速度的强大计算系统。的目标。目的是定量评估动态系统的连续部分对其离散部分行为的影响,并在此基础上对离散-连续系统的摄动运动数学模型进行分解的可能性。方法。这些措施旨在解决基于离散连续能力及其分解的问题。结果。对于三种由无穷维常微分方程系统描述的复杂动力系统,提出了连续部分对系统离散部分影响的定量评价。这些评估决定了这种系统的摄动运动数学模型的分解。创意。建立了三种离散-连续动力系统的简化数学模型。实用价值。所得结果可为货车在储罐中运输液体时的运动特性这门专业课的研究提供参考。通过MATLAB软件包的优化,可以同时模拟货车和被运输货物的各种参数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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