Теорема про реконструкцію деяких динамічних систем

• Main Author: Gorodetskyi, Viktor G.
• Format: Article
• Language: Ukrainian
• Published: The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2020
• Subjects: оригінальна система; диференціальна модель; реконструкція; спостережувана змінна; модель-кандидат; оригинальная система; дифференциальная модель; реконструкция; наблюдаемая переменная; original system; differential model; reconstruction; observed variable; candidate model
• Online Access: http://journal.iasa.kpi.ua/article/view/209145

A theorem which gives a rigorous justification for using the differential model to obtain an original system that describes a real physical process is proved. The theorem can be used to reconstruct the model from a single observed variable, the presence of which allows us to obtain a differential model. In the differential model, the variables that are missing are replaced by the time derivatives of the observed variable. The existence of relations that connect the original system and the differential model allows the transition from the differential model to the original system. In this case, several original candidate models can be obtained. As a result, the researcher can choose the model that most fully reflects the physics of the process. The proved theorem can also be used to simplify the previously obtained model, which probably contains redundant terms.