Integral dynamic models: theory and applications in the electric power industry

A brief overview of the methods of analysis of integral dynamic models and their applications is given. The modern foundations of the theory of linear and nonlinear integral equations used in modeling dynamic developing systems, including existence and uniqueness theorems for smooth and generalized solutions of the corresponding equations, are presented. A new formulation of the inverse problem and a numerical method for Volterra integral equations with piecewise continuous kernels are discussed for the case of the desired kernel discontinuity curves. The resulting integral equation is nonlinear with respect to discontinuity curves. Approximate and numerical methods for constructing solutions in irregular cases are proposed. Examples of integral dynamic models for cyber-physical systems and modeling of storage systems in the electric power industry are discussed.