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arXiv · 2609.37081

Optimal Actuator Design across Ranks and Control Horizons

Emmanuel Trélat·Enrique Zuazua
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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 $X=BB^\top$. Scalar actuators give rank-one matrices $X=bb^\top$; 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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Emmanuel Trélat, Enrique Zuazua. 2026-09-29. Optimal Actuator Design across Ranks and Control Horizons. https://arxiv.org/abs/2609.37081

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