This paper studies the trade-off between the degree of decentralization and the performance of a distributed controller in a linear-quadratic control setting. We study a system of interconnected agents over a graph and a distributed controller, called $\kappa$-distributed control, which lets the agents make control decisions based on the state information within distance $\kappa$ on the underlying graph. This controller can tune its degree of decentralization using the parameter $\kappa$ and thus allows a characterization of the relationship between decentralization and performance. We show that under mild assumptions, including stabilizability, detectability, and a subexponentially growing graph condition, the performance difference between $\kappa$-distributed control and centralized optimal control becomes exponentially small in $\kappa$. This result reveals that distributed control can achieve near-optimal performance with a moderate degree of decentralization, and thus it is an effective controller architecture for large-scale networked systems.
翻译:本文研究了在线性赤道控制环境下分散控制器的放权程度与分布式控制器的性能之间的权衡。 我们研究了一个图形和一个分布式控制器的互连代理器系统,称为 $\kappa美元分布式控制,让代理器根据在距离范围内的国家信息在基图上以$\kappa美元进行控制决策。 该控制器可以使用 $\kappa美元来调整其分散化程度,从而可以对分散化与绩效之间的关系进行定性。 我们显示,在温和的假设下,包括可稳定性、可探测性以及亚特性增长的图形状态下, $\kappa美元分配式控制与集中式最佳控制之间的性能差异在$\kappa美元中极小。 这一结果表明,分布式控制可以在适度的放权下实现接近最佳的性能,因此它是大型网络系统的有效控制器架构。