Learning-based DoS attack game strategy over multi-process systems

In cyber-physical systems, the state information from multiple processes is sent simultaneously to remote estimators through wireless channels. However, with the introduction of open media such as wireless networks, cyber-physical systems may become vulnerable to denial-of-service attacks, which can pose significant security risks and challenges to the systems. To better understand the impact of denial-of-service attacks on cyber-physical systems and develop corresponding defense strategies, several research papers have explored this issue from various perspectives. However, most current works still face three limitations. First, they only study the optimal strategy from the perspective of one side (either the attacker or defender). Second, these works assume that the attacker possesses complete knowledge of the system's dynamic information. Finally, the power exerted by both the attacker and defender is assumed to be small and discrete. All these limitations are relatively strict and not suitable for practical applications. In this paper, we addressed these limitations by establishing a continuous power game problem of a denial-of-service attack in a multi-process cyber-physical system with asymmetric information. We also introduced the concept of the age of information to comprehensively characterize data freshness. To solve this problem, we employed the multi-agent deep deterministic policy gradient algorithm. Numerical experiments demonstrate that the algorithm is effective for solving the game problem and exhibits convergence in multi-agent environments, outperforming other algorithms.