Stochastic Game in Linear Quadratic Gaussian Control for Wireless Networked Control Systems Under DoS Attacks

Recently, the security problem of wireless networked control systems (WNCSs) has become critical. In this article, we focus on strategies designing problem for sensor and denial-of-service (DoS) attacker in WNCS based on linear quadratic Gaussian (LQG) cost. In this scenario, a sensor measures the output of the system and transmits its local state estimate to the remote estimator via an unreliable channel which may suffer interference from an intelligent DoS attacker. In each step, the sensor demands to determine the power to transmit its packet data, at the same time, the attacker needs to determine the interference power to degrade the performance of the WNCS. To analyze this interactive decision-making process, we construct a two-player zero-sum stochastic game and propose an improved LQG cost considering energy-efficient factors. Then, for continuous power-level setting, we discuss the existence and the structure of equilibrium strategies of the sensor-attacker game. For a discrete power set, an algorithm is developed to solve equilibrium strategies for both players. Finally, we present an example to illustrate our results.