A Mathematical Cybersecurity Model of a Computer Network for the Control of Power Supply of Traction Substations

Based on the analysis of the problem of cybersecurity, it is shown that its solution is connected with the solution of a complex of interdependent problems whose features follow from the topology of a cyberspace. A graph is proposed that adequately reflects the topology of the computer network for the control of a system of power supply of traction substations and its mathematical model as the basis for the creation of modern cybersecurity models. The developed mathematical model of cybersecurity of a computer network is based on the theory of Pukhov’s differential transforms. The criterion of cybersecurity is formalized, and a minimax principle is proposed for the minimization of a functional in cases of worst combinations of intensities of flows of cyberattacks and protective actions. An intelligent method is developed to search for an optimal strategy for ensuring the cybersecurity of a computer network by the investigation of the functional formalized in this article for extremum.