Distributionally Robust Stackelberg Transactive Control Under Imperfect Price Signals

This paper develops a distributionally robust transactive control architecture that explicitly models ambiguity in the implementation of decentralized price signals in networked energy systems. Unlike conventional formulations that assume perfect signal execution, the proposed framework integrates a Wasserstein distributionally robust optimization (WDRO) layer based on an ambiguity set within a bilevel Stackelberg coordination structure, where uncertainty affects the executed price rather than only exogenous demand or generation. A tractable dual reformulation is derived, and the economic and physical layers are unified into a continuous-time dynamic system through predictive sensitivity coupling. Extensive parametric validation over ambiguity radius and perturbation levels identifies a robust operating region in which steady-state price volatility remains bounded while physical feasibility is preserved. The results also reveal a tuning-sensitive regime for very small ambiguity radii under nominal conditions, highlighting the role of distributional regularization in stabilizing coupled economic–physical dynamics. Overall, the proposed WDRO-based formulation provides system-level insight for coordination design under implementation-layer uncertainty in decentralized system-of-systems architectures, while remaining computationally tractable for large distribution networks.