Optimal Actuator Design across Ranks and Control Horizons
Trélat E, Zuazua E (2026)
Publication Language: English
Publication Status: Submitted
Publication Type: Unpublished / Preprint
Future Publication Type: Article in Edited Volumes
Publication year: 2026
URI: https://dcn.nat.fau.eu/wp-content/uploads/actuator.pdf
Open Access Link: https://arxiv.org/abs/2609.37081
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
Involved external institutions
France (FR)How to cite
APA:
Trélat, E., & Zuazua, E. (2026). Optimal Actuator Design across Ranks and Control Horizons. (Unpublished, Submitted).
MLA:
Trélat, Emmanuel, and Enrique Zuazua. Optimal Actuator Design across Ranks and Control Horizons. Unpublished, Submitted. 2026.
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