Safe adaptive NMPC using ellipsoidal tubes

TL;DR

This paper introduces a computationally efficient safe NMPC algorithm that uses ellipsoidal tubes to handle uncertainties and disturbances, ensuring constraint satisfaction, stability, and recursive feasibility in learning-based control.

Contribution

It presents a novel ellipsoidal tube-based NMPC method that accounts for uncertainties via successive linearization and set membership estimation, improving safety and scalability.

Findings

Algorithm guarantees recursive feasibility and stability.

Scales favorably with problem size.

Provides closed-loop performance guarantees.

Abstract

A computationally efficient nonlinear Model Predictive Control (NMPC) algorithm is proposed for safe learning-based 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.