Safe adaptive NMPC using ellipsoidal tubes

Conference item

Abstract:: A computationally efficient nonlinear Model Predictive Control (NMPC) algorithm is proposed for safe learningbased control with a system model represented by an incompletely known affine combination of basis functions and subject to additive set-bounded disturbances. The proposed algorithm employs successive linearization around predicted trajectories and accounts for the uncertain components of future states due to linearization, modelling errors and disturbances using ellipsoidal sets centered on the predicted nominal state trajectory. An ellipsoidal tube-based approach ensures satisfaction of constraints on control variables and model states. Feasibility is ensured using local bounds on linearization errors and a procedure based on a backtracking line search. We combine the approach with a set membership parameter estimation strategy in numerical simulations. We show that the ellipsoidal embedding of the predicted uncertainty scales favourably with the problem size. The resulting algorithm is recursively feasible and provides closed-loop stability and performance guarantees.

Files:: Buerger_and_Cannon_2025_Safe_adaptive_NMPC.pdf

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Notes:: This paper will be presented at the 23rd European Control Conferences, Thessaloniki, Greece, 24-27 June, 2025. This is the accepted manuscript version of the paper.
The author accepted manuscript (AAM) of this paper has been made available under the University of Oxford's Open Access Publications Policy, and a CC BY public copyright licence has been applied.

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