🤖 AI Summary
Characterizing the total information rate—a fundamental performance–sensitivity trade-off metric—in discrete-time control and filtering systems remains challenging, especially across linear time-invariant (LTI), linear time-varying (LTV), and nonlinear settings.
Method: We propose a novel analytical framework based on an extended I-MMSE relationship, generalizing the classical I-MMSE identity to discrete-time AWGN channels both with and without feedback. This unified information-theoretic approach integrates minimum mean-square error estimation, Kolmogorov–Bode-type spectral analysis, and optimal estimation theory.
Contribution/Results: Our framework yields exact analytical characterizations of the total information rate for broad classes of dynamical systems. It reveals fundamental limits on control and filtering performance and provides computable, tight information-rate bounds. By bridging information theory and control/estimation theory, this work establishes a new theoretical foundation for systematic design and trade-off analysis in networked and resource-constrained cyber-physical systems.
📝 Abstract
Fundamental limitations or performance trade-offs/limits are important properties and constraints of both control and filtering systems. Among various trade-off metrics, total information rate that characterizes the sensitivity trade-offs and time-averaged performance of control and filtering systems was conventionally studied by using the differential entropy rate and Kolmogorov-Bode formula. In this paper, by extending the famous I-MMSE (mutual information -- minimum mean-square error) 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 trade-off metric. Under this framework, we explore the trade-off properties of total information rate for a variety of the discrete-time control and filtering systems, e.g., LTI, LTV, and nonlinear, and propose an alternative approach to investigate total information rate via optimal estimation.
