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Publication Type: Unpublished / Preprint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

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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 (Unpublished, Submitted).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 Unpublished, Submitted. 2026.

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