This note considers the distributed optimal coordination (DOC) problem for heterogeneous linear multiagent systems. The local gradients are locally Lipschitz and the local convexity constants are unknown. A control law is proposed to drive the states of all agents to the optimal coordination that minimizes a global objective function. By exploring certain features of the invariant projection of the Laplacian matrix, the global asymptotic convergence is guaranteed utilizing only local interaction. The proposed control law is then extended with event-triggered communication schemes, which removes the requirement for continuous communications. Under the event-triggered control law, it is proved that no Zeno behavior is exhibited and the global asymptotic convergence is preserved. The proposed control laws are fully distributed, in the sense that the control design only uses the information in the connected neighborhood. Furthermore, to achieve the DOC for linear multiagent systems with unmeasurable states, an observer-based event-triggered control law is proposed. A simulation example is given to validate the proposed control laws.

中文翻译：

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具有事件触发机制的异构线性多智能体系统的分布式优化协调

本笔记考虑了异构线性多智能体系统的分布式最优协调 (DOC) 问题。局部梯度是局部 Lipschitz，局部凸性常数未知。提出了一种控制律来驱动所有代理的状态到最小化全局目标函数的最佳协调。通过探索拉普拉斯矩阵不变投影的某些特征，仅使用局部交互就可以保证全局渐近收敛。然后使用事件触发的通信方案扩展所提出的控制律，从而消除对连续通信的要求。在事件触发控制律下，证明了没有芝诺行为，保持全局渐近收敛。提议的控制律是完全分布式的，从某种意义上说，控制设计仅使用连接邻域中的信息。此外，为了实现状态不可测的线性多智能体系统的 DOC，提出了一种基于观察者的事件触发控制律。给出了一个仿真例子来验证所提出的控制规律。