This article is concerned with the co-design of fault detection and consensus control protocol for a class of multi-agent systems (MASs) subject to Denial-of-Service attack, where the attack behavior is hidden to the defender as the adversary may launch the attack with different durations but the defender may not know the real situation at each time instant. Due to the complicated attack behavior, a hidden semi-Markov process is introduced where only the observed attack modes emitted by the inaccessible ones are available. The probability density functions of sojourn time and the semi-Markov kernel are adopted to help analyze the combined fault detection and consensus control system. Sufficient conditions on the $\sigma $ -error mean square stability of MASs with mixed ${H_\infty }/{H_ {-} }$ performance are established by using a set of Lyapunov functions that depend on the hidden and the observed attack modes. Moreover, the gain matrices of controller and detector are obtained by solving an optimization problem with some matrix inequality constraints. Finally, the simulation of autonomous unmanned underwater vehicles is used to show the effectiveness of the proposed results.

中文翻译：

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隐藏式DoS攻击下多智能体系统故障检测与共识控制协议的协同设计

本文涉及针对遭受“拒绝服务”攻击的一类多代理系统（MAS）的故障检测和共识控制协议的协同设计，该攻击行为在防御者可能发动时对防御者隐藏了攻击行为攻击具有不同的持续时间，但防御者可能不知道每个时刻的真实情况。由于攻击行为复杂，因此引入了隐藏的半马尔可夫过程，其中仅可观察到的由无法访问的攻击模式发出的攻击模式可用。采用了停留时间和半马尔可夫核的概率密度函数，以帮助分析组合的故障检测和共识控制系统。充分条件 $ \ sigma $ 混合MAS的误差均方稳定性 $ {H_ \ infty} / {H_ {-}} $ 通过使用一组Lyapunov函数来确定性能，这些函数取决于隐藏和观察到的攻击模式。此外，通过解决具有一些矩阵不等式约束的优化问题，可以获得控制器和检测器的增益矩阵。最后，通过对无人驾驶水下航行器的仿真来证明所提出的结果的有效性。