  This paper studies the performance and resilience of a cyber-physical control
system (CPCS) with attack detection and reactive attack mitigation. It
addresses the problem of deriving an optimal sequence of false data injection
attacks that maximizes the state estimation error of the system. The results
provide basic understanding about the limit of the attack impact. The design of
the optimal attack is based on a Markov decision process (MDP) formulation,
which is solved efficiently using the value iteration method. Using the
proposed framework, we quantify the effect of false positives and
mis-detections on the system performance, which can help the joint design of
the attack detection and mitigation. To demonstrate the use of the proposed
framework in a real-world CPCS, we consider the voltage control system of power
grids, and run extensive simulations using PowerWorld, a high-fidelity power
system simulator, to validate our analysis. The results show that by carefully
designing the attack sequence using our proposed approach, the attacker can
cause a large deviation of the bus voltages from the desired setpoint. Further,
the results verify the optimality of the derived attack sequence and show that,
to cause maximum impact, the attacker must carefully craft his attack to strike
a balance between the attack magnitude and stealthiness, due to the
simultaneous presence of attack detection and mitigation.
