Data-Driven Optimal Distributed Controller Synthesis via Spatial Regret

In this paper, we present a novel method for synthesising an optimal distributed spatial regret controller using experimentally obtained frequency-response data. Spatial regret provides a measure of the performance gap between a structured distributed controller and an oracle with enhanced communication topology. We relax assumptions on the communication topology, allowing the oracle to adopt any enhanced structure. While this generalisation requires an iterative solution in place of a single convex program, we provide a tractable algorithm that synthesises optimal controllers from frequency-response data while preserving stability and the desired communication structure. Through numerical examples, we illustrate the better performance of the spatial regret controller compared to classical H2/Hinf designs, underscoring the effectiveness of the proposed methodology.