ADMM–EKI: Principled Refinement With Local Guarantees for Constrained Nonlinear MPC

This work studies constrained nonlinear model predictive control using ADMM with a derivative-free EKI inner solver in deterministic square-root form. The motivation is to obtain a principled zero-order refinement mechanism for sampling-based MPC: the Kalman update contracts the ensemble through residual-informed covariances and resembles a Gauss–Newton refinement under local linearization. Building on an earlier ADMM–EKI formulation that used heuristic scheduling and was empirically validated, this work develops a fixed-schedule variant and analyzes the resulting inexact outer iteration. The main contribution is an explicit inner forcing rule linking the EKI refinement budget to the ADMM tolerance sequence; under stated local assumptions, this yields augmented-Lagrangian descent up to summable error, residual convergence, and KKT characterization of accumulation points.