Оптимальне управління кібербезпекою: глобальна керованість лінійних моделей

In the age of digitalization, cybersecurity is critical for modern technological systems. The tasks of protecting information nodes, preventing the spread of cyberattacks, and restoring system functionality after successful attacks require studying the possibility of controlling dynamic processes. Mathematical models based on ordinary differential equations make it possible to describe and analyze these processes in terms of controllability. An extremely important property of cybersecurity models is their global controllability, which means that the system can be moved from any initial state to a desired end state using appropriately selected control. In the context of cybersecurity, this allows for an effective response to threats, recovery from attacks, and prevention of undesirable scenarios. This paper presents the conditions for global controllability of stationary and non-stationary linear systems of differential equations that model dynamic processes in the information space. The results obtained by different researchers are systematized, and the author presents his proof of some of them. Examples confirming the theory are constructed.