Parametric Reduction of Mathematical Models of Dynamic Systems

• Datum: 2018
• Hauptverfasser: Верлань, Андрей Анатолиевич, Дячук, Александр Анатолиевич, Палагина, Елена Анатолиевна, Палагин, Владимир Васильевич
• Format: Artikel
• Sprache: Russisch
• Veröffentlicht: Кам'янець-Подільський національний університет імені Івана Огієнка 2018
• Online Zugang: http://mcm-math.kpnu.edu.ua/article/view/159382
• Назва журналу: Mathematical and computer modelling. Series: Physical and mathematical sciences

The development of modern technical and information systems is characterized by increased requirements for the reliability of operation and reliability of the forecast of their dynamic characteristics. One of the conditions for such prediction is the construction of mathematical models, the parameters of which reflect real factors affecting the dynamics of the system. The construction of sufficiently accurate models is characterized by difficulties in their implementation and interaction of these systems with the external environment. To overcome these difficulties, modeling complexes are created, the design of which is based on the use of simplified mathematical models.With a variety of approaches used to simplify the mathematical models of the systems being studied, the simplification of a complex model is always based on some equivalence of the original and simplified model. Due to the fact that the estimation of equivalence of models is substantially determined by the objectives of the study system and the specificity of the original model, the classification of simplification methods according to equivalence models of models seems difficult. An analysis of known model simplification methods shows their main disadvantage, which is to compare full and simplified models with nominal values of system parameters. In the majority of methods, the task of accounting for the total error of estimating the quality indices of the systems under study is not included.In this paper it is accepted that a simplified model is equivalent to the original complete model in relation to the given quality indicators. This condition is fulfilled if the use of a simplified model instead of a complete does not require the relaxation of the specified limits on the accuracy of estimates of the quality indices of the system being studied.The principle of simplification of models is proposed, which consists in neglecting parameters, factors or fragments of the model, insignificant for the given indicators of quality. On this principle, a method for simplifying (reduction) of mathematical models is developed, differing from the known additional motion and the harmonization of the accuracy of the initial data and perturbations of the parameters with the required accuracy of estimates of the quality indices of the systems under study.