Spatiotemporal Response Decay for Near-Optimal Distributed LQR via System Level Synthesis
Abstract
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.
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BibTeX
@misc{zhou2026spatiotemporal,
title = {{Spatiotemporal Response Decay for Near-Optimal Distributed LQR via System Level Synthesis}},
author = {Chenchen Zhou and José Matias},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11699},
eprint = {2610.11699},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11699},
}
RIS
TY - UNPB
TI - Spatiotemporal Response Decay for Near-Optimal Distributed LQR via System Level Synthesis
AU - Chenchen Zhou
AU - José Matias
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11699
UR - https://arxiv.org/abs/2610.11699
AB - 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.
ER -