Automatic Nonlinear MPC Approximation With Closed-Loop Guarantees

• 成果类型: Article
• 署名作者: Tokmak, Abdullah; Fiedler, Christian; Zeilinger, Melanie N.; Trimpe, Sebastian; Kohler, Johannes
• 署名单位: Aalto University; RWTH Aachen University; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3558871
• 发表日期: 2025
• 页码: 6388-6403
• 关键词: Kernel; interpolation; Approximation Error; Approximation algorithms; Function approximation; Artificial neural networks; accuracy; safety; training; Predictive control; Constrained control; kernel-based function approximation; Machine Learning; nonlinear (NL) predictive control

摘要

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 tackle by proposing the Adaptive and Localized Kernel Interpolation Algorithm with eXtrapolated reproducing kernel Hilbert space norm, which we refer to as Alkia-x. Alkia-x is a noniterative 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-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.