Optimal Two Player LQR State Feedback With Varying Delay

TL;DR

This paper derives an explicit solution for a two-player distributed LQR problem with communication delays, showing that optimal controls are linear and depend on the current delay regime, extending dynamic programming methods.

Contribution

It introduces a novel explicit solution for two-player distributed LQR with varying delays, expanding dynamic programming techniques to handle delay-dependent control strategies.

Findings

Optimal controls are linear in information.

Controller dynamics are piecewise linear based on delay regimes.

Solution extends existing methods to variable delay scenarios.

Abstract

This paper presents an explicit solution to a two player distributed LQR problem in which communication between controllers occurs across a communication link with varying delay. We extend known dynamic programming methods to accommodate this varying delay, and show that under suitable assumptions, the optimal control actions are linear in their information, and that the resulting controller has piecewise linear dynamics dictated by the current effective delay regime.