Source and Citation
(Selected from Journal of Command and Control)
Citation: WU Xiaotai, YU Jinqi, TANG Yang, ZHANG Zhenhua. Consensus Analysis of Multi-agent Systems Based on Random Communication under Jamming Attack. Journal of Command and Control, 2023, 9(6): 726-733.
Abstract
In practical applications, multi-agent systems may be subject to sustained or intermittent malicious attacks over certain time intervals, causing communication channels between agents to be disrupted. To address this, it is assumed that communication times between agents are random, i.e., each communication interval consists of a deterministic preparation time plus a random communication interval, which reduces the risk of information being maliciously attacked during transmission. By using a ternary control approach and stochastic analysis techniques, sufficient conditions for consensus of multi-agent systems under jamming attacks are obtained. Numerical simulations are provided to validate the theoretical results.
Introduction
As future conflicts rapidly evolve toward information-centric and networked confrontation, swarm-intelligence techniques represented by multi-agent cooperative control are being integrated into military applications, including drone swarm tactics, coordinated missile engagements, and cooperative reconnaissance systems [1–3]. Specifically, swarm systems use network and communication technologies to enable information exchange and coordination between an agent and its neighbor nodes [4,5], thereby accomplishing complex missions.
Alongside the application of network technologies to swarm intelligence, command and control modules and communication channels face risks from external malicious attacks [6]. When a system is under network attack, legitimate operators may be unable to command or control the target system, causing control commands to fail to reach actuators and preventing consensus in multi-agent systems, which undermines swarm objectives. Ensuring the security of network communications in controlled systems thus remains a significant challenge.
Networked control systems can be threatened by various types of network attacks, primarily including denial-of-service (DoS) attacks, deception attacks, and jamming attacks [7–9]. Reference [10] studied secure estimation and control for cyber-physical systems under adversarial attacks, where control signals can be maliciously altered before reaching actuators. Reference [11] showed that attackers can inject false data into systems without being detected. Reference [12] pointed out that energy-limited attackers can use DoS attacks to block communications. Therefore, studying cooperative control, particularly consensus, of multi-agent systems under network attacks is important.
Recent research has made progress on consensus under stochastic network attacks, where attacks follow Bernoulli distributions or Markov chains [13–15]. Reference [13] analyzed the effect of DoS-induced packet loss on control performance and designed optimal attack schedules that maximize estimation error under energy constraints. Reference [14] designed intelligent attackers that randomly inject DoS to disconnect certain communication links, thereby disrupting consensus. Reference [15] considered risk-sensitive stochastic control under Markov-modulated DoS attack strategies using hidden Markov models to randomly block control packets.
However, prior work often focuses on how attackers optimize attack strategies, while fewer studies address how the attacked system can maintain operation under attack. Designing effective and implementable control mechanisms that allow the attacked system to continue functioning is valuable. Reference [16] proposed a randomized transmission protocol combined with triggering mechanisms to mitigate jamming effects on consensus.
Building on the ternary control method that generates three control signals via random communication or sampling among agents [17], this paper studies consensus of multi-agent systems under jamming attacks in two scenarios: when the attack onset and duration are independent of the random communication times, and when they are correlated. The randomized communication protocol in [16] can ensure bounded consensus in probability within finite time. However, [16] assumed the random communication sequence follows a uniform distribution, which may lead to unreasonably small or even overlapping adjacent communication intervals, limiting practical applicability.
This paper examines consensus for a class of multi-agent systems under jamming attacks using a random communication protocol. By applying a ternary control approach and stochastic analysis, sufficient conditions for consensus under jamming are obtained. Unlike [16], communication times here are modeled as a combination of a deterministic preparation time plus a random interval, further reducing the risk of information being attacked during transmission.
Notably, the hybrid interval composed of deterministic and random durations avoids excessively small or overlapping communication intervals present in [16], extending the applicability of related results. Compared with deterministic communication strategies in [17,18], the proposed mechanism makes sampling instants stochastic, which hinders an attacker from detecting or predicting the system's sampling pattern. Moreover, unlike results that guarantee asymptotic or exponential convergence over infinite time scales [19], the ternary control method here can ensure finite-time consensus for multi-agent systems.
