Separation is Optimal for LQR under Intermittent Feedback

TL;DR

This paper proves the optimality of separation for communication-constrained LQR problems with i.i.d. disturbances, deriving a threshold-based scheduling policy and a disturbance-independent linear controller.

Contribution

It establishes the separation principle under communication constraints and characterizes the optimal scheduling and control policies for such systems.

Findings

Separation principle holds for communication-constrained LQR with symmetric disturbances.

Optimal scheduling policy is a symmetric threshold rule on accumulated disturbance.

Optimal controller is a discounted linear feedback law independent of scheduling policy.

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.