This paper is concerned with the impulsive consensus tracking problem of Lipschitz nonlinear multi-agent systems subject to deception attacks. The proposed distributed impulsive tracking algorithm allows only partial state variables of every agent to be governed by consensus impulses. The considered deception attacks are supposed to take place in the controller–actuator channel, and can be modelled by a set of Bernoulli processes. By considering the discrete-time deception signal as bounded external disturbance, the consensus tracking problem reduces to the exponential input-to-state stable (EISS) problem of the tracking error system. The EISS-gain is used as an assessment index in measuring the capacity of consensus control laws for attenuating attacks. Specifically, a novel EISS analysis method combined with the use of a weighted discontinuous Lyapunov function is proposed to establish the consensus tracking criterion. A convex optimization problem with linear matrix inequalities-based constraints is formulated to design the guaranteed performance distributed impulsive controller, which makes the EISS-gain as small as possible. Two illustrated examples quantify the effectiveness of the proposed analysis and design approach.

本文关注受欺骗攻击的 Lipschitz 非线性多智能体系统的脉冲一致性跟踪问题。所提出的分布式脉冲跟踪算法只允许每个代理的部分状态变量受共识脉冲控制。所考虑的欺骗攻击应该发生在控制器-执行器通道中，并且可以通过一组伯努利过程进行建模。通过将离散时间欺骗信号视为有界外部干扰，一致性跟踪问题简化为跟踪误差系统的指数输入到状态稳定（EISS）问题。EISS 增益被用作衡量共识控制律减弱攻击能力的评估指标。具体来说，提出了一种新的 EISS 分析方法，结合使用加权不连续 Lyapunov 函数来建立一致性跟踪标准。提出了一个基于线性矩阵不等式约束的凸优化问题来设计保证性能的分布式脉冲控制器，使 EISS 增益尽可能小。两个图解的例子量化了所提出的分析和设计方法的有效性。