Automatic nonlinear MPC approximation with closed-loop guarantees
This addresses the need for efficient, safe control in domains such as robotics, though it is an incremental improvement on existing approximation methods.
The paper tackles the computational complexity of nonlinear model predictive control (MPC) in safety-critical systems like robotics by introducing ALKIA-X, an algorithm that automatically computes explicit approximations with closed-loop guarantees, demonstrating reduced computational demand in applications.
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.