Automatic nonlinear MPC approximation with closed-loop guarantees
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910405810454528 |
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| author | Tokmak, Abdullah Fiedler, Christian Zeilinger, Melanie N. Trimpe, Sebastian Köhler, Johannes |
| author_facet | Tokmak, Abdullah Fiedler, Christian Zeilinger, Melanie N. Trimpe, Sebastian Köhler, Johannes |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10199 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Automatic nonlinear MPC approximation with closed-loop guarantees Tokmak, Abdullah Fiedler, Christian Zeilinger, Melanie N. Trimpe, Sebastian Köhler, Johannes Systems and Control Machine Learning Optimization and Control 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. |
| title | Automatic nonlinear MPC approximation with closed-loop guarantees |
| topic | Systems and Control Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2312.10199 |