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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2411.05488 |
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| _version_ | 1866909912450203648 |
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| author | Iannucci, Andrea Crisan, Dan Cass, Thomas |
| author_facet | Iannucci, Andrea Crisan, Dan Cass, Thomas |
| contents | We use a rough path-based approach to investigate the degeneracy problem in the context of pathwise control. We extend the framework developed in arXiv:1902.05434 to treat admissible controls from a suitable class of Hölder continuous paths and simultaneously to handle a broader class of noise terms. Our approach uses fractional calculus to augment the original control equation, resulting in a system with added fractional dynamics. We adapt the existing analysis of fractional systems from the work of Gomoyunov arXiv:1908.01747, arXiv:2111.14400v1 , arXiv:2109.02451 to this new setting, providing a notion of a rough fractional viscosity solution for fractional systems that involve a noise term of arbitrarily low regularity. In this framework, following the method outlined in arXiv:1902.05434, we derive sufficient conditions to ensure that the control problem remains non-degenerate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05488 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pathwise Optimal Control and Rough Fractional Hamilton-Jacobi-Bellman Equations for Rough-Fractional Dynamics Iannucci, Andrea Crisan, Dan Cass, Thomas Optimization and Control We use a rough path-based approach to investigate the degeneracy problem in the context of pathwise control. We extend the framework developed in arXiv:1902.05434 to treat admissible controls from a suitable class of Hölder continuous paths and simultaneously to handle a broader class of noise terms. Our approach uses fractional calculus to augment the original control equation, resulting in a system with added fractional dynamics. We adapt the existing analysis of fractional systems from the work of Gomoyunov arXiv:1908.01747, arXiv:2111.14400v1 , arXiv:2109.02451 to this new setting, providing a notion of a rough fractional viscosity solution for fractional systems that involve a noise term of arbitrarily low regularity. In this framework, following the method outlined in arXiv:1902.05434, we derive sufficient conditions to ensure that the control problem remains non-degenerate. |
| title | Pathwise Optimal Control and Rough Fractional Hamilton-Jacobi-Bellman Equations for Rough-Fractional Dynamics |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2411.05488 |