A Game of Drones: Cyber-Physical Security of Time-Critical UAV Applications with Cumulative Prospect Theory Perceptions and Valuations

In this paper, a novel mathematical framework is introduced for modeling and analyzing the cyber-physical security of time-critical UAV applications. A general UAV security network interdiction game is formulated to model interactions between a UAV operator and an interdictor, each of which can be benign or malicious. In this game, the interdictor chooses the optimal location(s) from which to target the drone system by interdicting the potential paths of the UAVs. Meanwhile, the UAV operator responds by finding an optimal path selection policy that enables its UAVs to evade attacks and minimize their mission completion time. New notions from cumulative prospect theory (PT) are incorporated into the game to capture the operator's and the interdictor's subjective valuations of mission completion times and perceptions of the risk levels facing the UAVs. The equilibrium of the game, with and without PT, is then analytically characterized and studied, while providing detailed derivations of mission completion times (and their expected values), PT valuations of both players (along with proofs of their convergence), and equilibrium points under different studied security regimes. Novel algorithms are then proposed to reach the game's equilibria under both PT and classical game theory. Simulation results show the properties of the equilibrium for both the rational and PT cases, highlighting the effects of bounded rationality on the interdictor's and the operator's strategies as well as mission completion times, and the way it can be exploited by a fully rational opponent.