Automatic nonlinear MPC approximation with closed-loop guarantees

TL;DR

This paper introduces ALKIA-X, a novel non-iterative algorithm that efficiently approximates nonlinear MPC controllers with guaranteed bounds, enabling real-time safety-critical control applications.

Contribution

The paper presents ALKIA-X, a new algorithm for automatic explicit approximation of nonlinear MPC with closed-loop safety guarantees, reducing computational complexity for high-rate control.

Findings

ALKIA-X provides fast, well-conditioned approximations of nonlinear MPC.

The method guarantees bounds on approximation error.

Demonstrated reduced computation in realistic control scenarios.

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.