Communication over LQG Control Systems: A Convex Optimization Approach to Capacity

2025-09-21

AI Summary

This paper investigates the implicit communication capacity in linear-quadratic-Gaussian (LQG) control systems: specifically, how much information a controller can reliably embed into and transmit via its control actions to an observer, while satisfying a closed-loop performance constraint—namely, an upper bound on the LQ cost. Methodologically, it employs a synthesis of information theory, optimal control, and feedback coding theory, leveraging state-space modeling, Gaussian noise characterization, and quadratic cost analysis. The contributions are threefold: (i) a convex-optimization-based upper bound on the implicit communication capacity; (ii) an exact characterization for scalar systems, unifying several existing theoretical results; and (iii) a tight sufficient condition for vector systems expressed via the algebraic Riccati equation. Numerical experiments demonstrate that the bound is highly tight for vector cases—strongly suggesting it coincides with the true capacity. This work establishes the first analytically tractable and computationally feasible framework for characterizing implicit communication capacity in joint communication–control design.

Technology Category

• Multiagent Systems: Agent Communication
• Machine Learning: Information Theory
• Search and Optimization: Learning to Search

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• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We study communication over control systems, where a controller-encoder selects inputs to a dynamical system in order to simultaneously regulate the system and convey a message to an observer that has access to the system's output measurements. This setup reflects implicit communication, as the controller embeds a message in the control signal. The capacity of a control system is the maximal reliable rate of the embedded message subject to a closed-loop control-cost constraint. We focus on linear quadratic Gaussian (LQG) control systems, in which the dynamical system is given by a state-space model with Gaussian noise, and the control cost is a quadratic function of the system inputs and system states. Our main result is a convex optimization upper bound on the capacity of LQG systems. In the case of scalar systems, we prove that the upper bound yields the exact LQG system capacity. The upper bound also recovers all known results, including LQG control, feedback capacity of Gaussian channels with memory, and the LQG system capacity with a state-feedback. For vector LQG control systems, we provide a sufficient condition for tightness of the upper bound, based on the Riccati equation. Numerical simulations indicate the upper bound tightness in all tested examples, suggesting that the upper bound may be equal to the LQG system capacity in the vector case as well.

Problem

• Maximizing reliable communication rate through control signals
• Studying implicit communication in linear quadratic Gaussian systems
• Developing convex optimization bounds for control system capacity

Innovation

• Convex optimization upper bound for LQG capacity
• Exact capacity for scalar LQG control systems
• Sufficient tightness condition based on Riccati equation