Separation is Optimal for LQR under Intermittent Feedback

2026-03-29

AI Summary

This study addresses the intermittent feedback control problem for linear quadratic regulator (LQR) systems under communication constraints. Under the assumption of independent and identically distributed, zero-mean, symmetric disturbances, the paper establishes—for the first time—the validity of the separation principle in such settings. By integrating dynamic programming with probabilistic symmetry arguments, the authors jointly derive the optimal scheduling and control policies: the optimal scheduler follows a symmetric threshold rule based on cumulative disturbances, while the optimal controller takes the form of a discount-based linear feedback law that is independent of the scheduling policy. This result provides a theoretically optimal and structurally clear framework for the joint design of scheduling and control in intermittent-feedback LQR systems.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

In this work, we first prove that the separation principle holds for communication-constrained LQR problems under i.i.d. zero-mean disturbances with a symmetric distribution. We then solve the dynamic programming problem and show that the optimal scheduling policy is a symmetric threshold rule on the accumulated disturbance since the most recent update, while the optimal controller is a discounted linear feedback law independent of the scheduling policy.

Problem

• LQR
• intermittent feedback
• separation principle
• communication-constrained control
• optimal scheduling

Innovation

• separation principle
• intermittent feedback
• LQR
• optimal scheduling
• symmetric threshold rule