Robust Data-Driven Control Against Actuator FDI for Unknown Linear Systems

This paper designs a data-driven controller for unknown linear systems whose actuators suffer from false data injection (FDI) attacks, using only noisy input-state data. To achieve this objective, a general FDI attack model is introduced, which imposes constraints only on the switching frequency of attack channels and the magnitude of attack matrices. A time-varying state feedback control law is designed based on offline and online input-state data, which adapts to the channel switching of FDI attacks. This is achieved by solving a data-based semi-definite programs (SDPs) on-the-fly such that stabilizing the set of subsystems consistent with both offline clean data and online attack-corrupted data. It is shown that under mild conditions on the attack and the noise, the feasibility of the proposed SDP guarantees that the controller stabilizes the attack-corrupted system. A numerical example is presented to validate the effectiveness of the proposed method.