Stealthy Hacking and Secrecy of Controlled State Estimation Systems With Random Dropouts

We study the maximum information gain that an adversary may obtain through hacking without being detected. Consider a dynamical process observed by sensor transmits local estimate of system state to remote estimator according some reference transmission policy across packet-dropping wireless channel equipped with acknowledgments (ACK). An overhears transmissions and proactively hijacks reprogram its policy. define perfect secrecy as keeping averaged expected error covariance bounded at legitimate unbounded adversary. By analyzing stationary distribution covariance, we show can be attained for unstable systems only if ACK has no packet dropouts. In other situations, prove independent detection methods, is not attainable. For this scenario, devise Stackelberg game derive optimal defensive present branch-and-bound algorithm global optimality solve proposed game.