Replay attack detection using a zonotopic KF and LQ approach

This paper exploits the analogy between the stochastic and zonotopic Kalman filters with the aim of formulating a metric that allows to assess the impact of an external zonotopically bounded signal in an state estimate optimal control scheme. To that end, the concept of linear quadratic zonotopic (LQZ) controller is introduced. Besides, the design of a zonotopically bounded watermarking signal such that enforces replay attack detectability is also addressed. The proposed detection scheme takes advantage of the observability loss of an a priori known exogenous signal during the replay phase of the attack. Consequently, by injecting the corresponding estimation error generated by a set-based observer, a zonotopically bounded signal such that imposes replay attack detectability is achieved. A numerical example is provided.