Automatic Nonlinear MPC Approximation With Closed-Loop Guarantees

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 <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Alkia-x</small>, the Adaptive and Localized Kernel Interpolation Algorithm with eXtrapolated reproducing kernel Hilbert space norm. <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Alkia-x</small> is a non-iterative algorithm that ensures well-conditioned computations, a fast-to-evaluate approximating function, and the guaranteed satisfaction of any desired bound on the approximation error. Hence, <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Alkia-x</small> automatically computes an explicit function that approximates the MPC, yielding a controller suitable for safety-critical systems and high sampling rates. We apply <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Alkia-x</small> to approximate two nonlinear MPC schemes, demonstrating reduced computational demand and applicability to realistic problems.