Single-Letterization of Rate-Cost Tradeoffs in Static Time-Invariant Control (STIC) Systems
Abstract
In settings such as online recommendation platforms, medical decision-making with interim summaries, and stochastic control with static plants, the underlying system is often static so that the next state depends only on the most recent action. Moreover, the true system state is high-dimensional and cannot be observed directly, so actions must be selected based on information received through a rate-limited communication link, which constrains the control performance. This leads to a fundamental rate-cost tradeoffunicodex2014the minimum communication rate required to achieve a prescribed average control cost. We study this tradeoff for a class of static systems we term static time-invariant control (STIC) systems, namely, control systems in which the next state depends on the history only through the most recent control action via a time-invariant kernel. For general control systemsunicodex2014not necessarily static or time-invariantunicodex2014our prior work characterized this tradeoff through the limit of a sequence of directed-information minimization problems. However, the dimension of these problems grows with the time horizon, making the limiting formulation computationally intractable. In the present paper, we show for STIC systems that this growing-size formulation admits a single-letter characterization. This identifies STIC systems as the control-side counterpart of Noisy Output is the STate (NOST) channelsunicodex2014one of the few channel models whose feedback capacity admits a single-letter characterization. This yields, to our knowledge, the first constant-size convex characterization of the rateunicodex2013cost tradeoff beyond linear quadratic Gaussian (LQG) control.
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BibTeX
@misc{atay2026singleletterization,
title = {{Single-Letterization of Rate-Cost Tradeoffs in Static Time-Invariant Control (STIC) Systems}},
author = {Eray Unsal Atay and Venkat Chandrasekaran and Victoria Kostina},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22789},
eprint = {2610.22789},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22789},
}
RIS
TY - UNPB
TI - Single-Letterization of Rate-Cost Tradeoffs in Static Time-Invariant Control (STIC) Systems
AU - Eray Unsal Atay
AU - Venkat Chandrasekaran
AU - Victoria Kostina
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.22789
UR - https://arxiv.org/abs/2610.22789
AB - In settings such as online recommendation platforms, medical decision-making with interim summaries, and stochastic control with static plants, the underlying system is often static so that the next state depends only on the most recent action. Moreover, the true system state is high-dimensional and cannot be observed directly, so actions must be selected based on information received through a rate-limited communication link, which constrains the control performance. This leads to a fundamental rate-cost tradeoffunicodex2014the minimum communication rate required to achieve a prescribed average control cost. We study this tradeoff for a class of static systems we term static time-invariant control (STIC) systems, namely, control systems in which the next state depends on the history only through the most recent control action via a time-invariant kernel. For general control systemsunicodex2014not necessarily static or time-invariantunicodex2014our prior work characterized this tradeoff through the limit of a sequence of directed-information minimization problems. However, the dimension of these problems grows with the time horizon, making the limiting formulation computationally intractable. In the present paper, we show for STIC systems that this growing-size formulation admits a single-letter characterization. This identifies STIC systems as the control-side counterpart of Noisy Output is the STate (NOST) channelsunicodex2014one of the few channel models whose feedback capacity admits a single-letter characterization. This yields, to our knowledge, the first constant-size convex characterization of the rateunicodex2013cost tradeoff beyond linear quadratic Gaussian (LQG) control.
ER -