Controlling Chaotic Maps using Next-Generation Reservoir Computing
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917580751503360 |
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| author | Kent, Robert M. Barbosa, Wendson A. S. Gauthier, Daniel J. |
| author_facet | Kent, Robert M. Barbosa, Wendson A. S. Gauthier, Daniel J. |
| contents | In this work, we combine nonlinear system control techniques with next-generation reservoir computing, a best-in-class machine learning approach for predicting the behavior of dynamical systems. We demonstrate the performance of the controller in a series of control tasks for the chaotic Hénon map, including controlling the system between unstable fixed-points, stabilizing the system to higher order periodic orbits, and to an arbitrary desired state. We show that our controller succeeds in these tasks, requires only 10 data points for training, can control the system to a desired trajectory in a single iteration, and is robust to noise and modeling error. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_03813 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Controlling Chaotic Maps using Next-Generation Reservoir Computing Kent, Robert M. Barbosa, Wendson A. S. Gauthier, Daniel J. Machine Learning Neural and Evolutionary Computing Systems and Control Chaotic Dynamics In this work, we combine nonlinear system control techniques with next-generation reservoir computing, a best-in-class machine learning approach for predicting the behavior of dynamical systems. We demonstrate the performance of the controller in a series of control tasks for the chaotic Hénon map, including controlling the system between unstable fixed-points, stabilizing the system to higher order periodic orbits, and to an arbitrary desired state. We show that our controller succeeds in these tasks, requires only 10 data points for training, can control the system to a desired trajectory in a single iteration, and is robust to noise and modeling error. |
| title | Controlling Chaotic Maps using Next-Generation Reservoir Computing |
| topic | Machine Learning Neural and Evolutionary Computing Systems and Control Chaotic Dynamics |
| url | https://arxiv.org/abs/2307.03813 |