Kernel-Based Optimal Control: An Infinitesimal Generator Approach
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866910918441435136 |
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| author | Bevanda, Petar Hoischen, Nicolas Wittmann, Tobias Brüdigam, Jan Hirche, Sandra Houska, Boris |
| author_facet | Bevanda, Petar Hoischen, Nicolas Wittmann, Tobias Brüdigam, Jan Hirche, Sandra Houska, Boris |
| contents | This paper presents a novel operator-theoretic approach for optimal control of nonlinear stochastic systems within reproducing kernel Hilbert spaces. Our learning framework leverages data samples of system dynamics and stage cost functions, with only control penalties and constraints provided. The proposed method directly learns the infinitesimal generator of a controlled stochastic diffusion in an infinite-dimensional hypothesis space. We demonstrate that our approach seamlessly integrates with modern convex operator-theoretic Hamilton-Jacobi-Bellman recursions, enabling a data-driven solution to the optimal control problems. Furthermore, our learning framework includes nonparametric estimators for uncontrolled infinitesimal generators as a special case. Numerical experiments, ranging from synthetic differential equations to simulated robotic systems, showcase the advantages of our approach compared to both modern data-driven and classical nonlinear programming methods for optimal control. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01591 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kernel-Based Optimal Control: An Infinitesimal Generator Approach Bevanda, Petar Hoischen, Nicolas Wittmann, Tobias Brüdigam, Jan Hirche, Sandra Houska, Boris Optimization and Control Machine Learning Robotics Systems and Control This paper presents a novel operator-theoretic approach for optimal control of nonlinear stochastic systems within reproducing kernel Hilbert spaces. Our learning framework leverages data samples of system dynamics and stage cost functions, with only control penalties and constraints provided. The proposed method directly learns the infinitesimal generator of a controlled stochastic diffusion in an infinite-dimensional hypothesis space. We demonstrate that our approach seamlessly integrates with modern convex operator-theoretic Hamilton-Jacobi-Bellman recursions, enabling a data-driven solution to the optimal control problems. Furthermore, our learning framework includes nonparametric estimators for uncontrolled infinitesimal generators as a special case. Numerical experiments, ranging from synthetic differential equations to simulated robotic systems, showcase the advantages of our approach compared to both modern data-driven and classical nonlinear programming methods for optimal control. |
| title | Kernel-Based Optimal Control: An Infinitesimal Generator Approach |
| topic | Optimization and Control Machine Learning Robotics Systems and Control |
| url | https://arxiv.org/abs/2412.01591 |