2025/10/01 by Ahmed Abdelhady A. Khalil, Khalil, Ahmed, Mohamed Safwat +3
Engineering · #Advanced Control Systems Optimization #FOS: Electrical engineering #FOS: Mathematics #Fault Detection and Control Systems #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2510.00559
openalex publication_date 2025/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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, stage-wise nonlinear inequality constraints in the NMPC problem are embedded via an augmented Lagrangian with nonnegative slack variables. We then show that the resulting unconstrained augmented-Lagrangian primal subproblem admits a Bayesian interpretation: under independent Gaussian virtual observations, its minimizers coincide with MAP estimators, enabling solution via EKI. However, since the nonnegativity constraint on the slacks is a hard constraint not naturally encoded by a Gaussian model, our proposed algorithm yields a two-block ADMM scheme that alternates between (i) an inexact primal step that minimizes the augmented-Lagrangian objective (implemented via EKI rollouts), (ii) a nonnegativity projection for the slacks, and (iii) a dual ascent step. To balance exploration and convergence, an annealing schedule tempers sampling covariances while a penalty schedule increases constraint enforcement over outer iterations, encouraging global search early and precise constraint satisfaction later. We evaluate the proposed controller on a 6-DOF UR5e manipulation benchmark in MuJoCo, comparing it against DIAL-MPC (an iterative MPPI variant) as the arm traverses a cluttered tabletop environment.