Physics-informed Gaussian Processes as Linear Model Predictive Controller
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909713285775360 |
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| author | Tebbe, Jörn Besginow, Andreas Lange-Hegermann, Markus |
| author_facet | Tebbe, Jörn Besginow, Andreas Lange-Hegermann, Markus |
| contents | We introduce a novel algorithm for controlling linear time invariant systems in a tracking problem. The controller is based on a Gaussian Process (GP) whose realizations satisfy a system of linear ordinary differential equations with constant coefficients. Control inputs for tracking are determined by conditioning the prior GP on the setpoints, i.e. control as inference. The resulting Model Predictive Control scheme incorporates pointwise soft constraints by introducing virtual setpoints to the posterior Gaussian process. We show theoretically that our controller satisfies open-loop stability for the optimal control problem by leveraging general results from Bayesian inference and demonstrate this result in a numerical example. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_04502 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Physics-informed Gaussian Processes as Linear Model Predictive Controller Tebbe, Jörn Besginow, Andreas Lange-Hegermann, Markus Optimization and Control Machine Learning Systems and Control We introduce a novel algorithm for controlling linear time invariant systems in a tracking problem. The controller is based on a Gaussian Process (GP) whose realizations satisfy a system of linear ordinary differential equations with constant coefficients. Control inputs for tracking are determined by conditioning the prior GP on the setpoints, i.e. control as inference. The resulting Model Predictive Control scheme incorporates pointwise soft constraints by introducing virtual setpoints to the posterior Gaussian process. We show theoretically that our controller satisfies open-loop stability for the optimal control problem by leveraging general results from Bayesian inference and demonstrate this result in a numerical example. |
| title | Physics-informed Gaussian Processes as Linear Model Predictive Controller |
| topic | Optimization and Control Machine Learning Systems and Control |
| url | https://arxiv.org/abs/2412.04502 |