Automatic nonlinear MPC approximation with closed-loop guarantees

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.