Automatic nonlinear MPC approximation with closed-loop guarantees

arXiv (Cornell University)

Abstract

Safety guarantees are vital in many control applications, such as robotics. Model predictive control (MPC) provides a constructive framework for controlling safety-critical systems, but is limited by its computational complexity. We address this problem by presenting a novel algorithm that automatically computes an explicit approximation to nonlinear MPC schemes while retaining closed-loop guarantees. Specifically, the problem can be reduced to a function approximation problem, which we then tackle by proposing ALKIA-X, the Adaptive and Localized Kernel Interpolation Algorithm with eXtrapolated reproducing kernel Hilbert space norm. ALKIA-X is a non-iterative algorithm that ensures numerically well-conditioned computations, a fast-to-evaluate approximating function, and the guaranteed satisfaction of any desired bound on the approximation error. Hence, ALKIA-X automatically computes an explicit function that approximates the MPC, yielding a controller suitable for safety-critical systems and high sampling rates. We apply ALKIA-X to approximate two nonlinear MPC schemes, demonstrating reduced computational demand and applicability to realistic problems.

Authors 5

1. Abdullah Tokmak
2. Christian Fiedler Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering , RWTH Aachen University , 52068 Aachen , Germany,

3. Melanie N. Zeilinger

   ETH Zurich · Institute for Biomedical Engineering

   Affiliation as printed

   Institute for Dynamic Systems and Control , ETH Zurich , Zurich CH-8092 , Switzerland,

4. Sebastian Trimpe Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering , RWTH Aachen University , 52068 Aachen , Germany,

5. Johannes Köhler