Denial-of-Service Security Attack in the Continuous-Time World

Hybrid systems are integrations of discrete computation and continuous physical evolution. The physical components of such systems introduce safety requirements, the achievement of which asks for the correct monitoring and control from the discrete controllers. However, due to denial-of-service security attack, the expected information from the controllers is not received and as a consequence the physical systems may fail to behave as expected. This paper proposes a formal framework for expressing denial-of-service security attack in hybrid systems. As a virtue, a physical system is able to plan for reasonable behavior in case the ideal control fails due to unreliable communication, in such a way that the safety of the system upon denial-of-service is still guaranteed. In the context of the modeling language, we develop an inference system for verifying safety of hybrid systems, without putting any assumptions on how the environments behave. Based on the inference system, we implement an interactive theorem prover and have applied it to check an example taken from train control system.