In this paper, we address the problem of automatically approximating
nonlinear model predictive control (MPC) schemes with closed-loop guarantees.
First, we discuss how this 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. In a numerical experiment, we apply ALKIA-X to a nonlinear MPC
scheme, demonstrating reduced offline computation and online evaluation time
compared to a state-of-the-art method.

本文中，我们解决了自动近似带有闭环保证的非线性模型预测控制（MPC）方案的问题。我们提出了 ALKIA-X 算法，它是一种自适应和本地化的核插值算法，可以将此问题简化为函数近似问题，并确保数值计算条件良好、近似函数计算速度快，并保证近似误差满足任何期望的边界。因此，ALKIA-X 可以自动计算出一个显式函数来近似 MPC，从而产生适用于安全关键系统和高采样率的控制器。在数值实验中，我们将 ALKIA-X 应用于一个非线性 MPC 方案，与最先进的方法相比，显示了离线计算和在线评估时间的减少。