In this paper, a cooperative Linear Quadratic Regulator (LQR) problem is investigated for multi-input systems, where each input is generated by an agent in a network. The input matrices are different and locally possessed by the corresponding agents respectively, which can be regarded as different ways for agents to control the multi-input system. By embedding a fully distributed information fusion strategy, a novel cooperative LQR-based controller is proposed. Each agent only needs to communicate with its neighbors, rather than sharing information globally in a network. Moreover, only the joint controllability is required, which allows the multi-input system to be uncontrollable for every single agent or even all its neighbors. In particular, only one-time information exchange is necessary at every control step, which significantly reduces the communication consumption. It is proved that the boundedness (convergence) of the controller gains is guaranteed for time-varying (time-invariant) systems. Furthermore, the control performance of the entire system is ensured. Generally, the proposed controller achieves a better trade-off between the control performance and the communication overhead, compared with the existing centralized/decentralized/consensus-based LQR controllers. Finally, the effectiveness of the theoretical results is illustrated by several comparative numerical examples.

中文翻译：

---

多输入时变系统的全分布式基于 LQR 的控制器设计

在本文中，针对多输入系统研究了协作线性二次调节器 (LQR) 问题，其中每个输入都由网络中的代理生成。不同的输入矩阵分别由相应的智能体局部拥有，可以看作智能体控制多输入系统的不同方式。通过嵌入完全分布式信息融合策略，提出了一种新型的基于协作 LQR 的控制器。每个代理只需要与其邻居通信，而不是在网络中全局共享信息。此外，只需要联合可控性，这使得多输入系统对于每个单独的代理甚至它的所有邻居都是不可控的。特别是，在每个控制步骤只需要一次信息交换，这大大减少了通信消耗。证明了控制器增益的有界性（收敛性）对于时变（时不变）系统是有保证的。此外，保证了整个系统的控制性能。通常，与现有的集中式/分散式/基于共识的 LQR 控制器相比，所提出的控制器在控制性能和通信开销之间实现了更好的折衷。最后，通过几个比较数值例子说明了理论结果的有效性。与现有的集中式/分散式/基于共识的 LQR 控制器相比，所提出的控制器在控制性能和通信开销之间实现了更好的折衷。最后，通过几个比较数值例子说明了理论结果的有效性。与现有的集中式/分散式/基于共识的 LQR 控制器相比，所提出的控制器在控制性能和通信开销之间实现了更好的折衷。最后，通过几个比较数值例子说明了理论结果的有效性。