Data-Driven Stochastic Optimal Control in Reproducing Kernel Hilbert Spaces
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909878859071488 |
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| author | Hoischen, Nicolas Bevanda, Petar Sosnowski, Stefan Hirche, Sandra Houska, Boris |
| author_facet | Hoischen, Nicolas Bevanda, Petar Sosnowski, Stefan Hirche, Sandra Houska, Boris |
| contents | This paper proposes a fully data-driven approach for optimal control of nonlinear control-affine systems represented by a stochastic diffusion. The focus is on the scenario where both the nonlinear dynamics and stage cost functions are unknown, while only a control penalty function and constraints are provided. To this end, we embed state probability densities into a reproducing kernel Hilbert space (RKHS) to leverage recent advances in operator regression, thereby identifying Markov transition operators associated with controlled diffusion processes. This operator learning approach integrates naturally with convex operator-theoretic Hamilton-Jacobi-Bellman recursions that scale linearly with state dimensionality, effectively solving a wide range of nonlinear optimal control problems. Numerical results demonstrate its ability to address diverse nonlinear control tasks, including the depth regulation of an autonomous underwater vehicle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16407 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Data-Driven Stochastic Optimal Control in Reproducing Kernel Hilbert Spaces Hoischen, Nicolas Bevanda, Petar Sosnowski, Stefan Hirche, Sandra Houska, Boris Optimization and Control Machine Learning Systems and Control This paper proposes a fully data-driven approach for optimal control of nonlinear control-affine systems represented by a stochastic diffusion. The focus is on the scenario where both the nonlinear dynamics and stage cost functions are unknown, while only a control penalty function and constraints are provided. To this end, we embed state probability densities into a reproducing kernel Hilbert space (RKHS) to leverage recent advances in operator regression, thereby identifying Markov transition operators associated with controlled diffusion processes. This operator learning approach integrates naturally with convex operator-theoretic Hamilton-Jacobi-Bellman recursions that scale linearly with state dimensionality, effectively solving a wide range of nonlinear optimal control problems. Numerical results demonstrate its ability to address diverse nonlinear control tasks, including the depth regulation of an autonomous underwater vehicle. |
| title | Data-Driven Stochastic Optimal Control in Reproducing Kernel Hilbert Spaces |
| topic | Optimization and Control Machine Learning Systems and Control |
| url | https://arxiv.org/abs/2407.16407 |