Abstract This paper investigates the cooperative output regulation problem of heterogeneous linear multi-agent systems under singular dynamics and adaptive distributed protocol. Considering the followers do not know the matrix information of the leader, two novel adaptive distributed protocols are developed based on the state and measurement output. Then, as the technology basis of the cooperative output regulation strategy of the singular multi-agent systems considered in this paper, some stability analysis results of linear time-varying singular systems are proved. Next, sufficient conditions are established to solve the cooperative output regulation problem of heterogeneous singular multi-agent systems with the adaptive distributed protocols designed in this paper. The general entirety method is proposed, which avoids the design of standard reduction transformation matrices, the calculation of model reduction and the impulse-free hypothesis in the standard reduction method. Finally, numerical results are provided to demonstrate the feasibility and effectiveness of the proposed techniques.

中文翻译：

---

自适应分布式协议下奇异多智能体系统的协同输出调节和一般整体法

摘要 本文研究了奇异动力学和自适应分布式协议下异构线性多智能体系统的协同输出调节问题。考虑到追随者不知道领导者的矩阵信息，基于状态和测量输出开发了两种新颖的自适应分布式协议。然后，作为本文考虑的奇异多智能体系统协同输出调节策略的技术基础，证明了线性时变奇异系统的一些稳定性分析结果。接下来，建立充分条件来解决具有本文设计的自适应分布式协议的异构奇异多智能体系统的协作输出调节问题。提出了一般的整体方法，避免了标准归约变换矩阵的设计、模型归约的计算和标准归约方法中的无脉冲假设。最后，提供了数值结果来证明所提出技术的可行性和有效性。