Denial-of-Service Attacks on Cyber-Physical Systems Against Linear Quadratic Control: A Stackelberg-Game Analysis

Abstract

This article concentrates on the linear quadratic control of cyber-physical systems subject to denial-of-service attacks. A Stackelberg game framework is proposed to analyze the strategic interaction between a sensor and an attacker considering a standard block fading wireless communication channel. The reward function composing of the linear quadratic control consumption and the power consumption is provided on account of energy constraints of the sensor and the attacker. To proactively overcome the difficulty in characterizing or computing the Stackelberg equilibrium (SE), the formulated game is actively transformed into a Markov decision process under a restricted information structure, enabling the extraction of essential SE properties. In addition, the reward function is approximated to derive an analytical expression of a suboptimal SE of the game based on an approximate dynamic programming. As a special case, the investigation also delves into the capacity achieving coding scheme. Finally, numerical examples are provided to illustrate the effectiveness of the obtained results.