| In this dissertation, we analyze the performance of Cyber-Physical Systems (CPSs) in adversarial environments for four different scenarios. We further provide either robust algorithm design which can withstand the attack or countermeasure which helps to detect the presence of the attack.;For static detection, we provide the optimal policy for the adversary and prove that the optimal detector is a constant detector based purely on a-prior information when the adversary compromises no less than half of the sensors. When the adversary compromises less than half sensors, we prove that the optimal detector must be of a special form based on a Hamming-like distant. We also provide the optimal detector for the boundary case and a heuristic detector for general cases.;For static estimation, we prove that the optimal estimator is a constant estimator based on the a-prior distribution if no less than half of the sensors are compromised. If less than half sensor is compromised, then the optimal estimator is given by the solution of a minimax problem. We prove that with additional constraints, the minimax problem can be further simplified.;We further consider linear dynamical systems, where we discuss two possible attack scenarios: the replay attack and the integrity attack. We provide a necessary and sufficient condition under which the replay attack is feasible and proposed two countermeasures that can effectively detect the replay, at the expense of control performance. For integrity attack, we provide a numerical method, based on ellipsoid approximation, to quantify the performance degradation of the CPS under the attack based on the concept of reachable set. We also prove a necessary and sufficient condition under which the attacker could destabilize the system without being detected. |
