Robust adaptive NMPC using ellipsoidal tubes

Journal article

We propose a computationally efficient nonlinear Model Predictive Control (NMPC) algorithm for safe, learningbased control. The system model is represented as an affine combination of basis functions with unknown parameters, and is subject to additive set-bounded disturbances. Our algorithm employs successive linearization around nominal predicted trajectories and accounts for uncertainties in predicted states due to linearization, model errors, and disturbances using ellipsoidal sets. The ellipsoidal tube-based approach ensures that constraints on control inputs and system states are satisfied. Robustness to uncertainty is ensured using bounds on linearization errors and a backtracking line search. We show that the ellipsoidal embedding of model uncertainty scales favourably with system dimensions in numerical simulations. The algorithm incorporates set membership parameter estimation, and provides guarantees of recursive feasibility and input-to-state practical stability

Authors: Buerger, J; Cannon, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IEEE
• Journal: IEEE Transactions on Automatic Control
• Publication date: 2026-03-09
• Acceptance date: 2026-03-04
• DOI: 10.1109/tac.2026.3672069
• EISSN: 1558-2523
• ISSN: 0018-9286
• Language: English
• Keywords: convex optimization; nonlinear model predictive control; optimization; trajectory; uncertainty; numerical stability; adaptation models; predictive models; prediction algorithms; adaptive control; tube model predictive control; stability criteria; predictive control; perturbation methods