Abstract This paper investigates the time-varying formation tracking (TVFT) control problem considering a constant input delay and unknown external disturbances for the general linear multi-agent system (MAS) under a directed communication graph containing a spanning tree. To achieve that, a new time-varying shape format is firstly proposed. Then, a disturbance observer (DO) is introduced to compensate the unknown disturbance effect. After that, the Artstein’s model reduction technique is adopted and modified to design a state predictor in order to transform the MAS with a delayed input into a delay-free system. Fourthly, an adaptive observer (AO), which is used to estimate the designed state predictor, is proposed by using the neighbors’ information such as the inputs, time-varying shapes, DOs, AOs and relative state measurements. The convergence of closed-loop system is guaranteed by the designed algebraic Riccati equation. The whole controller requires no eigenvalue information of the Laplacian matrix of communication graph, thus is fully distributed. Finally, the effectiveness of proposed fully distributed controller (FDC) is verified by numerical examples and factors influencing FDC performances are analyzed.

中文翻译：

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具有输入延迟和扰动的线性多智能体系统的全分布式时变编队跟踪控制

摘要 本文研究了一般线性多智能体系统（MAS）在包含生成树的有向通信图下考虑恒定输入延迟和未知外部干扰的时变编队跟踪（TVFT）控制问题。为此，首先提出了一种新的时变形状格式。然后，引入干扰观测器（DO）来补偿未知的干扰影响。之后，采用并修改 Artstein 的模型缩减技术来设计状态预测器，以便将具有延迟输入的 MAS 转换为无延迟系统。第四，通过使用邻居的信息，如输入、时变形状、DO、AO 和相对状态测量，提出了一种用于估计设计状态预测器的自适应观测器 (AO)。闭环系统的收敛性由设计的代数Riccati方程保证。整个控制器不需要通信图拉普拉斯矩阵的特征值信息，因此是完全分布式的。最后，通过数值例子验证了所提出的完全分布式控制器（FDC）的有效性，并分析了影响 FDC 性能的因素。