Automatic Nonlinear MPC Approximation With Closed-Loop Guarantees

IEEE Transactions on Automatic Control, vol. 70, pp. 6388–6403

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 proposingAlkia-x, the Adaptive and Localized Kernel Interpolation Algorithm with eXtrapolated reproducing kernel Hilbert space norm.Alkia-xis a non-iterative algorithm that ensures well-conditioned computations, a fast-to-evaluate approximating function, and the guaranteed satisfaction of any desired bound on the approximation error. Hence,Alkia-xautomatically computes an explicit function that approximates the MPC, yielding a controller suitable for safety-critical systems and high sampling rates. We applyAlkia-xto approximate two nonlinear MPC schemes, demonstrating reduced computational demand and applicability to realistic problems.

Authors 5

1. Abdullah Tokmak

   Aalto University

   Affiliation as printed

   Department of Electrical Engineering and Automation, Aalto University, Espoo, Finland

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, Aachen, Germany

3. Melanie N. Zeilinger

   ETH Zurich · Institute for Dynamic Systems and Control

   Affiliation as printed

   Institute for Dynamic Systems and Control, ETH Zürich, Zürich, Switzerland

   Institute for Dynamic Systems and Control, ETH Zurich, Zurich, 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, Aachen, Germany

5. Johannes Köhler

   ETH Zurich · Institute for Dynamic Systems and Control

   Affiliation as printed

   Institute for Dynamic Systems and Control, ETH Zürich, Zürich, Switzerland

   Institute for Dynamic Systems and Control, ETH Zurich, Zurich, Switzerland