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Approaches to the Development of Complex Systems Models

机译：开发复杂系统模型的方法

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The paper discusses the problem of mathematical formalization and creation of models of complex systems. It is noted that depending on the availability of information on the properties of the system, various approaches to the development of its models are possible including the systematization of problem statements in terms of a priori information about the object. Features of the development and possibilities of using mathematical models in the conditions of detailed, partial and missing a priori information about the properties of the system are described. Special attention is paid to the problem of creating adequate models of complex systems under uncertainty. Examples of such systems are natural systems, modern industrial enterprises, socio-economic systems. Perspectivity of the cybernetic principle of the “black box” is indicated, when the structure of the model is set by a certain universal mathematical model without reference to the structure of a real object, and the parameters are determined knowing the reaction to known input effects. From the user's point of view, the model structure hidden in the “black box” imitates the behavioral features of a complex system. Such models are called information models. Classes of problems of reconstruction of model equations of complex systems are formed. Examples of solving problems (in the study of real complex processes) based on information models are given. It is noted that the key point in the development of the information model is to check its suitability for the solution of the practical problem associated with the assessment of adequacy in relation to the properties of the object of interest. Examples of different types of adequacy areas are given and also their features are given.
机译：本文讨论了数学形式化和创建复杂系统模型的问题。应当指出，根据有关系统属性的信息的可用性，可能有多种方法来开发其模型，包括根据有关对象的先验信息对问题陈述进行系统化。描述了在详细，部分和缺少有关系统属性的先验信息的条件下使用数学模型的开发特点和可能​​性。要特别注意在不确定性下创建复杂系统的适当模型的问题。这样的系统的例子是自然系统，现代工业企业，社会经济系统。当模型的结构是由某个通用数学模型设置的，而不参考真实对象的结构，并且确定了参数时就知道了对已知输入效应的反应，从而表明了“黑匣子”控制论原理的透视性。从用户的角度来看，隐藏在“黑匣子”中的模型结构模仿了复杂系统的行为特征。这种模型称为信息模型。形成了复杂系统模型方程重构的问题类。给出了基于信息模型解决问题的实例（在研究实际复杂过程中）。应当指出，信息模型开发的关键点是检查其是否适合解决与感兴趣对象的属性有关的充分性评估相关的实际问题。给出了不同类型的充足区域的示例，并给出了它们的特征。

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