发表机构
KU Leuven; Department of Chemical Engineering, KU Leuven（荷语鲁汶大学; 荷语鲁汶大学化学工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对网络化LQR问题，用系统级综合方法证明集中式响应的时空指数衰减界，据此设计近最优分布式控制器，数值实验验证了架构选择的指导因素。
AI 中文摘要
分布式控制需要确定信息的传播距离与保留时长。针对网络化线性二次调节（LQR）问题，我们采用系统级综合（System Level Synthesis）方法，限定每个节点相对于集中式控制的性能损失对应的资源范围。在满足可镇定、可检测性等均匀正则性假设的局部耦合系统中，我们证明集中式最优状态及输入对扰动脉冲的响应在时间和空间距离上均满足指数衰减界。在邻域规模呈多项式增长的网络中，充足的通信范围与记忆时域随容差的倒数呈对数增长，且与网络规模无关。截断这些响应可得到局部有限记忆滤波器，在可计算的小增益条件下具备稳定性与性能保证。在额外的均匀局部反馈条件下，我们还得到能将标称扰动效应限制在空间内并在有限时间内消除的控制器。数值实验展示了性能与扰动抑制需求如何指导架构选择。
英文摘要
Distributed control requires choosing how far information travels and how long it is retained. For networked linear quadratic regulation (LQR), we use System Level Synthesis to bound these resources for a specified performance loss per node relative to centralized control. For locally coupled systems under uniform regularity assumptions, including stabilizability and detectability, we prove that the centralized optimal state and input responses to disturbance impulses satisfy exponential decay bounds in both time and spatial distance. On networks with polynomial neighborhood growth, sufficient communication ranges and memory horizons grow logarithmically with the inverse tolerance, independently of network size. Truncating these responses gives local finite-memory filters with stability and performance guarantees under a computable small-gain condition. Under an additional uniform local feedback condition, we also obtain controllers that confine nominal disturbance effects in space and eliminate them in finite time. Numerical experiments illustrate how performance and disturbance containment requirements guide architecture selection.
Comments31 pages, 8 figures. Code and data: https://github.com/Daakuang/spacetime-sls
