Optimal distributed LQG state feedback with varying communication delay

Abstract

This paper presents an explicit solution to a two player distributed LQG problem in which communication between controllers occurs across a communication link with varying delay. We extend known dynamic programming methods to accommodate this time-varying delay, and show that the resulting optimal controller has a piecewise linear structure, with control actions dictated by the current and next delay regime. By treating the next delay regime as a disturbance in the dynamic programming argument, we then derive the optimal causal controller.