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Contemporary Methods for Nonlinear Crisp and Fuzzy Dynamic Models: Theory and Applications

The purpose of this project is to study mathematical models of power systems with energy storage and electrical load leveling using modern methods of nonlinear analysis. The models under study are based on the Volterra integral equations with discontinuous kernels. The project is aimed at solving these classes in linear, non-linear and multidimensional cases, as well as in the case of systems of integral equations. In recent years, fuzzy mathematics has found wide application in various fields of science and technology. It is known that fuzzy dynamic systems allow describing a wider range of problems than classical dynamic systems. Thus, in this project, using the capabilities of this research group, fuzzy dynamic systems will be investigated for solving load-covering energy problems. Some numerical and semi-analytical methods will be developed to solve these problems in both crisp and fuzzy cases, such as the homotopy analysis method, the homotopy perturbation method, the extension method, the Adom decomposition method, the variational iteration method, and the collocation method. In addition, the CESTAC method and the CADNA library will be used to dynamically estimate the rounding error. These methods will be used to solve linear and non-linear problems of large dimensions. The effectiveness of the theory and numerical methods proposed in the project will be demonstrated in the management of hybrid networks, including those based on fuzzy controllers.

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