Qualitative Planning in Imperfect Information Games with Active Sensing and Reactive Sensor Attacks: Cost of Unawareness

We consider the probabilistic planning problem where the agent (called Player 1, or P1) can jointly plan the control actions and sensor queries in a sensor network and an attacker (called player 2, or P2) can carry out attacks on the sensors. We model such an adversarial interaction using a formal model -- a reachability game with partially controllable observation functions. The main contribution of this paper is to assess the cost of P1's unawareness: Suppose P1 misinterprets the sensor failures as probabilistic node failures due to unreliable network communication, and P2 is aware of P1's misinterpretation in addition to her partial observability. Then, from which states can P2 carry out sensor attacks to ensure, with probability one, that P1 will not be able to complete her reachability task even though, due to misinterpretation, P1 believes that she can almost-surely achieve her task. We develop an algorithm to solve the almost-sure winning sensor-attack strategy given P1's observation-based strategy. Our attack analysis could be used for attack detection in wireless communication networks and the design of provably secured attack-aware sensor allocation in decision-theoretic models for cyber-physical systems.