Automatic nonlinear MPC approximation with closed-loop guarantees

• URL: http://arxiv.org/abs/2312.10199v2
• Date: Thu, 11 Apr 2024 16:22:54 GMT
• Title: Automatic nonlinear MPC approximation with closed-loop guarantees
• Abstract summary: Model predictive control (MPC) provides a constructive framework for controlling safety-critical systems. We address this problem by presenting a novel algorithm that automatically computes an explicit approximation to nonlinear MPC schemes. We apply ALKIA-X to approximate two nonlinear MPC schemes, demonstrating reduced computational demand and applicability to realistic problems.
• Score: 7.98874664486269
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

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