Data-driven linear quadratic regulator design for unknown linear systems against false data injection attack

Among the diverse forms of cyber-attacks, false data injection (FDI) attacks are prone to occur and have become prominent threats. The present paper is concerned with the design of data-driven controllers of unknown cyber physical systems (CPSs) subjected to FDI attacks, using input-state data but no model knowledge. A core aspect of this issue revolves around the modelling of unknown FDI attacked system in the context of data-driven control. To solve the problem, we formulate an FDI attacks as a convex optimisation problem using the H2-norm, a FDI attacks channel model, and stability constraints. First, based on the input-state data sequences, the optimal feedback control law is designed to minimise the H2-norm of the closed-loop system's transfer function. The attacker's capability is modelled as a bounded constraint on attack power. The Schur complement lemma and a regularisation term provide sufficient conditions for the Schur stability of the FDI attacked system. The effectiveness of the proposed approach can be proved through a numerical example.