Ensemble Kalman Inversion for Constrained Nonlinear MPC: An ADMM-Splitting Approach

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Hauptverfasser: Khalil, Ahmed, Safwat, Mohamed, Bakolas, Efstathios
Format: Preprint
Veröffentlicht: 2025
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author Khalil, Ahmed
Safwat, Mohamed
Bakolas, Efstathios
author_facet Khalil, Ahmed
Safwat, Mohamed
Bakolas, Efstathios
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_00559
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Ensemble Kalman Inversion for Constrained Nonlinear MPC: An ADMM-Splitting Approach
Khalil, Ahmed
Safwat, Mohamed
Bakolas, Efstathios
Optimization and Control
Systems and Control
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.
title Ensemble Kalman Inversion for Constrained Nonlinear MPC: An ADMM-Splitting Approach
topic Optimization and Control
Systems and Control
url https://arxiv.org/abs/2510.00559