Optimal stealthy actuator attack design for cyber–physical systems: A reachable set reshaping approach

The security of cyber–physical systems faces critical challenges from stealthy attacks, which can inflict system damage while evading detection. Investigating attack strategies provides valuable insights for bolstering system defense. To this end, this paper proposes an optimal stealthy actuator attack design framework. First, the attack strategy is designed based on the reachable set (RS) analysis framework. By designing actuator attacks, a tight ellipsoidal outer approximation of the physical-state RS is reshaped toward the unsafe region. To avoid being detected by the χ 2 detector, the attack stealthiness condition is rigorously transformed into a linear matrix inequality (LMI) constraint on the actuator attack parameters. Consequently, the attack synthesis is formulated as a constrained optimization problem, aiming to reduce the conservatism of the attacked RS outer approximation while requiring this tight outer bound to extend beyond the prescribed safe boundary and enforcing the derived LMI-based condition for evading the χ 2 detector. An algorithmic solution is developed to synthesize the optimal attack parameters. Simulation results are given to demonstrate the effectiveness of the proposed optimal attack strategies.