Stealth and Detection of Edge Attacks for Networked Control Systems Under Optimal Control Energy: A Stackelberg Game Approach

ABSTRACT This paper investigates the stealth and detection of edge attacks for networked control systems. Firstly, the stealthiness and detectability of edge attacks are conceptualized as resources possessed by the attacker and the detector, respectively. A Stackelberg game framework is employed to model the resource allocation strategies of both players. In this framework, the attacker allocates resources to different edges to conceal the attack, which consequently leads to an increase in the control energy of the networked control system. In response, the detector allocates resources based on the attacker's strategy with the objective of identifying the attack and subsequently minimizing the control energy of the system. Secondly, when the attacker's resources are subject to either soft constraints (i.e., penalty terms in the objective function) or hard constraints (i.e., feasibility region limitations), constrained optimization methods are adopted to solve for the Stackelberg equilibrium. In particular, for the case with hard constraints, a tiered resource allocation strategy is proposed for the attacker to enhance the efficiency of computing the equilibrium under rigid resource limitations. Furthermore, to evaluate the payoffs of both players in the game, the scenario in which edge attacks are detected within the networked control system is formulated as a constrained optimization problem aimed at minimizing control energy. An equivalent reformulation and convex relaxation are then applied to derive an efficient solution to the resulting optimization problem. Finally, numerical simulations are conducted to validate the effectiveness of the proposed methods.