Distributed Formation Model Predictive Control Under Communication Denial: An Edge-Splitting ADMM with Centralized-Equivalence Gating and Confidence-Decayed Coupling

Distributed model predictive control (MPC) coordinates constrained multi-agent systems while preserving computational locality, yet an implementation can cease to represent its stated convex program. We study a minimal linear plant so communication denial is a modeled source of uncertainty, and treat centralized equivalence as a hard gate: an edge-splitting consensus alternating direction method of multipliers (ADMM) formulation of the formation-tracking quadratic program is built so every distributed update can be audited against a centralized solver. Against a Lagrangian dual-decomposition baseline, ADMM attains the same accuracy without step-size tuning. Across topologies, horizons, penalties, budgets, and denial windows, the exact branch matches the centralized optimum to numerical precision, the equivalence gate and saturation signature survive scaling to eight agents, and the saturation signature also survives measurement noise. For communication denial, we prove a bounded-error result separating the summable-error regime, which recovers the optimum exactly, from the merely-bounded regime, whose limit points remain O(ε)-optimal. Coupling each edge weight to message age through an exponentially decaying confidence factor contracts the distributed problem to uncoupled local MPC, so formation error saturates as outages lengthen; a fixed-weight ablation isolates this decay as the causal mechanism. We contribute a reproducible baseline and two honest mechanisms—centralized-equivalence gating and confidence-decayed coupling—for distributed formation MPC.