An Information-Theoretic Analysis of Discrete-Time Control and Filtering Limitations by the I-MMSE Relationships

• 成果类型: Article
• 署名作者: Wan, Neng; Li, Dapeng; Hovakimyan, Naira; Voulgaris, Petros G.
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign; Southern University of Science & Technology; Nevada System of Higher Education (NSHE); University of Nevada Reno
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3553075
• 发表日期: 2025
• 页码: 5926-5940
• 关键词: filtering; Information rates; control systems; entropy; Information theory; Mutual information; measurement; AWGN channels; Linear systems; Time-domain analysis; Control and filtering limits; fundamental limitations; mutual information-minimum mean-square error (I-MMSE) relationships; information-theoretic method; optimal estimation; total information rate

摘要

Fundamental limitations or performance tradeoffs/limits are important properties and constraints of both control and filtering systems. Among various tradeoff metrics, total information rate that characterizes the sensitivity tradeoffs and time-averaged performance of control and filtering systems was conventionally studied by using the differential entropy rate and Kolmogorov-Bode formula. In this article, by extending the famous mutual information-minimum mean-square error (I-MMSE) relationships to the discrete-time additive white Gaussian channels with and without feedback, a new paradigm is introduced to estimate and analyze total information rate as a control and filtering tradeoff metric. Under this framework, we explore the tradeoff properties of total information rate for a variety of the discrete-time control and filtering systems, e.g., linear time-invariant, linear time-varying, and nonlinear, and propose an alternative approach to investigate total information rate via optimal estimation.