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Optimal Actuator Design across Ranks and Control Horizons
Abstract
We study how actuator rank and control horizon jointly determine worst-case control performance for finite-dimensional linear systems under a fixed total actuator-gain budget. The design variable is the input covariance X=BB⊤. Scalar actuators give rank-one matrices X=bb⊤; dropping the rank constraint yields their convex hull and a semidefinite benchmark. We identify regimes in which low-rank designs necessarily fall short and others in which they attain the benchmark. At small time, the relaxed maximizer is unique and full rank. If A is cyclic, then, for every $k
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BibTeX
@misc{trelat2026optimal,
title = {{Optimal Actuator Design across Ranks and Control Horizons}},
author = {Emmanuel Trélat and Enrique Zuazua},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37081},
eprint = {2609.37081},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05768606v1},
}
RIS
TY - UNPB
TI - Optimal Actuator Design across Ranks and Control Horizons
AU - Emmanuel Trélat
AU - Enrique Zuazua
PY - 2026
DA - 2026/09/29
PB - HAL
DO - 10.48550/arxiv.2609.37081
UR - https://hal.science/hal-05768606v1
AB - We study how actuator rank and control horizon jointly determine worst-case control performance for finite-dimensional linear systems under a fixed total actuator-gain budget. The design variable is the input covariance X=BB^⊤. Scalar actuators give rank-one matrices X=bb^⊤; dropping the rank constraint yields their convex hull and a semidefinite benchmark. We identify regimes in which low-rank designs necessarily fall short and others in which they attain the benchmark. At small time, the relaxed maximizer is unique and full rank. If A is cyclic, then, for every $k
ER -