System identification with binary-valued observations under both denial-of-service attacks and data tampering attacks: the optimality of attack strategy

With the development of wireless communication technology, cyber physical systems are applied in various fields such as industrial production and infrastructure, where lots of information exchange brings cyber security threats to the systems. From the perspective of system identification with binary-valued observations, we study the optimal attack problem when the system is subject to both denial of service attacks and data tampering attacks. The packet loss rate and the data tampering rate caused by the attack is given, and the estimation error is derived. Then the optimal attack strategy to maximize the identification error with the least energy is described as a min-max optimization problem with constraints. The explicit expression of the optimal attack strategy is obtained. Simulation examples are presented to verify the effectiveness of the main conclusions.