Annealed Ensemble Kalman Inversion for Constrained Nonlinear Model Predictive Control: An ADMM Approach

This work proposes a novel Alternating Direction Method of Multipliers (ADMM)-based Ensemble Kalman Inversion (EKI) algorithm for solving constrained nonlinear model predictive control (NMPC) problems. First, the stage-wise nonlinear inequality constraints in the NMPC problem are embedded via an augmented Lagrangian with nonnegative slack variables. We then show that the unconstrained augmented Lagrangian formulation of the NMPC admits a Bayesian interpretation: under a Gaussian observation model, its minimizers coincide with MAP estimators, enabling solution via EKI. However, since the nonnegativity constraint on the slacks cannot be enforced via Gaussian noise, our proposed algorithm results in a two-block ADMM that alternates between (i) a primal step that minimizes the unconstrained augmented Lagrangian, (ii) a nonnegativity projection for the slacks, and (iii) a dual ascent step. To balance exploration and convergence, an annealing schedule tempers covariances and penalty weights, thereby encouraging global search early and precise constraint satisfaction later. To demonstrate the performance of the proposed method, we compare it with another iterative sampling-based approach based on Model Predictive Path Integral (MPPI) control, called DIAL-MPC.