  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.
