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.

翻译：安全保证在机器人学等许多控制应用中至关重要。模型预测控制（MPC）为安全关键系统的控制提供了结构化框架，但其计算复杂度限制了应用。我们提出一种新算法，可在保留闭环保证的同时自动计算非线性MPC方案的显式近似。具体而言，该问题可简化为函数逼近问题，我们通过提出ALKIA-X（自适应局部化核插值算法与外推再生核希尔伯特空间范数）来解决它。ALKIA-X是一种非迭代算法，能确保数值计算条件良好、近似函数评估速度快，并且保证任意期望的逼近误差边界得以满足。因此，ALKIA-X自动计算显式函数来近似MPC，从而生成适用于安全关键系统和高采样率的控制器。我们将ALKIA-X应用于两个非线性MPC方案的近似，证明了其降低计算需求的优势以及对实际问题的适用性。