This paper investigates the problem of secure consensus tracking for positive multi-agent systems (MASs) under periodic denial-of-service (DoS) attacks, where DoS attacks usually impede the transmission of signals between agents. The considered DoS attacks in this paper are assumed to recur periodically, guided by a time-sequence approach. Firstly, an observer-based output-feedback consensus tracking algorithm is proposed to ensure that all state variables within each agent in positive MAS are accurately tracked to the agent at the origin. Moreover, the frequency and average paralyzed time of DoS attacks are also carefully analyzed, and some sufficient conditions for the positivity and stability of the MAS are provided by resorting to positive system theory and Lyapunov stability theory. It is proven that all signals of positive MAS can be tracked to the target origin position. Finally, two simulations are presented to illustrate the theoretical results.

中文翻译：

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周期性拒绝服务攻击下积极多智能体系统基于观察者的安全共识跟踪

本文研究了周期性拒绝服务 (DoS) 攻击下主动多代理系统 (MAS) 的安全共识跟踪问题，其中 DoS 攻击通常会阻碍代理之间的信号传输。本文中考虑的 DoS 攻击假设在时间序列方法的指导下周期性地重复发生。首先，提出了一种基于观察者的输出反馈一致性跟踪算法，以确保正 MAS 中每个智能体内的所有状态变量都准确地跟踪到原点的智能体。此外，还仔细分析了DoS攻击的频率和平均瘫痪时间，并利用正系统理论和Lyapunov稳定性理论为MAS的积极性和稳定性提供了一些充分条件。事实证明，所有正MAS信号都可以跟踪到目标原点位置。最后，给出了两个模拟来说明理论结果。