Reactive Synthesis of Sensor Revealing Strategies in Hypergames on Graphs

In many security applications of cyber-physical systems, a system designer must guarantee that critical missions are satisfied against attacks in the sensors and actuators of the CPS. Traditional security design of CPSs often assume that attackers have complete knowledge of the system. In this article, we introduce a class of deception techniques and study how to leverage asymmetric information created by deception to strengthen CPS security. Consider an adversarial interaction between a CPS defender and an attacker, who can perform sensor jamming attacks. To mitigate such attacks, the defender introduces asymmetrical information by deploying a "hidden sensor," whose presence is initially undisclosed but can be revealed if queried. We introduce hypergames on graphs to model this game with asymmetric information. Building on the solution concept called subjective rationalizable strategies in hypergames, we identify two stages in the game: An initial game stage where the defender commits to a strategy perceived rationalizable by the attacker until he deviates from the equilibrium in the attacker's perceptual game; Upon the deviation, a delay-attack game stage starts where the defender plays against the attacker, who has a bounded delay in attacking the sensor being revealed. Based on backward induction, we develop an algorithm that determines, for any given state, if the defender can benefit from hiding a sensor and revealing it later. If the answer is affirmative, the algorithm outputs a sensor revealing strategy to determine when to reveal the sensor during dynamic interactions. We demonstrate the effectiveness of our deceptive strategies through two case studies related to CPS security applications.