Nonparametric Adaptive Control and Prediction: Theory and Randomized Algorithms
2021 60th IEEE Conference on Decision and Control (CDC) December 13-15, 2021. Austin, Texas
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IEEE|2021 60th IEEE Conference on Decision and Control (CDC)
2024
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| Online Access: | https://hdl.handle.net/1721.1/155760 |
| _version_ | 1826205523603619840 |
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| author | Boffi, Nicholas M. Tu, Stephen Slotine, Jean-Jacques |
| author2 | Massachusetts Institute of Technology. Nonlinear Systems Laboratory |
| author_facet | Massachusetts Institute of Technology. Nonlinear Systems Laboratory Boffi, Nicholas M. Tu, Stephen Slotine, Jean-Jacques |
| author_sort | Boffi, Nicholas M. |
| collection | MIT |
| description | 2021 60th IEEE Conference on Decision and Control (CDC) December 13-15, 2021. Austin, Texas |
| first_indexed | 2024-09-23T13:14:24Z |
| format | Article |
| id | mit-1721.1/155760 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2025-02-19T04:22:11Z |
| publishDate | 2024 |
| publisher | IEEE|2021 60th IEEE Conference on Decision and Control (CDC) |
| record_format | dspace |
| spelling | mit-1721.1/1557602025-01-05T04:43:16Z Nonparametric Adaptive Control and Prediction: Theory and Randomized Algorithms Boffi, Nicholas M. Tu, Stephen Slotine, Jean-Jacques Massachusetts Institute of Technology. Nonlinear Systems Laboratory 2021 60th IEEE Conference on Decision and Control (CDC) December 13-15, 2021. Austin, Texas — A key assumption in the theory of nonlinear adaptive control is that the uncertainty of the system can be expressed in the linear span of a set of known basis functions. While this assumption leads to efficient algorithms, it limits applications to very specific classes of systems. We introduce a novel nonparametric adaptive algorithm that learns an infinite-dimensional parameter density to cancel an unknown disturbance in a reproducing kernel Hilbert space. Surprisingly, the resulting control input admits an analytical expression that enables its implementation despite its underlying infinite-dimensional structure. While this adaptive input is rich and expressive – subsuming, for example, traditional linear parameterizations – its computational complexity grows linearly with time, making it comparatively more expensive than its parametric counterparts. Leveraging the theory of random Fourier features, we provide an efficient randomized implementation which recovers the computational complexity of classical parametric methods while provably retaining the expressiveness of the nonparametric input. In particular, our explicit bounds only depend polynomially on the underlying parameters of the system, allowing our proposed algorithms to efficiently scale to high-dimensional systems. As an illustration of the method, we demonstrate the ability of the algorithm to learn a predictive model for a 60-dimensional system consisting of ten point masses interacting through Newtonian gravitation. 2024-07-23T16:28:00Z 2024-07-23T16:28:00Z 2021-12-14 2024-07-23T16:23:03Z Article http://purl.org/eprint/type/ConferencePaper https://hdl.handle.net/1721.1/155760 Boffi, Nicholas M., Tu, Stephen and Slotine, Jean-Jacques. 2021. "Nonparametric Adaptive Control and Prediction: Theory and Randomized Algorithms." 00. en 10.1109/cdc45484.2021.9682907 Creative Commons Attribution-Noncommercial-ShareAlike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf IEEE|2021 60th IEEE Conference on Decision and Control (CDC) Author |
| spellingShingle | Boffi, Nicholas M. Tu, Stephen Slotine, Jean-Jacques Nonparametric Adaptive Control and Prediction: Theory and Randomized Algorithms |
| title | Nonparametric Adaptive Control and Prediction: Theory and Randomized Algorithms |
| title_full | Nonparametric Adaptive Control and Prediction: Theory and Randomized Algorithms |
| title_fullStr | Nonparametric Adaptive Control and Prediction: Theory and Randomized Algorithms |
| title_full_unstemmed | Nonparametric Adaptive Control and Prediction: Theory and Randomized Algorithms |
| title_short | Nonparametric Adaptive Control and Prediction: Theory and Randomized Algorithms |
| title_sort | nonparametric adaptive control and prediction theory and randomized algorithms |
| url | https://hdl.handle.net/1721.1/155760 |
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