Robustly Learning Regions of Attraction from Fixed Data
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909311475646464 |
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| author | Tacchi, Matteo Lian, Yingzhao Jones, Colin |
| author_facet | Tacchi, Matteo Lian, Yingzhao Jones, Colin |
| contents | While stability analysis is a mainstay for control science, especially computing regions of attraction of equilibrium points, until recently most stability analysis tools always required explicit knowledge of the model or a high-fidelity simulator representing the system at hand. In this work, a new data-driven Lyapunov analysis framework is proposed. Without using the model or its simulator, the proposed approach can learn a piece-wise affine Lyapunov function with a finite and fixed off-line dataset. The learnt Lyapunov function is robust to any dynamics that are consistent with the off-line dataset, and its computation is based on second order cone programming. Along with the development of the proposed scheme, a slight generalization of classical Lyapunov stability criteria is derived, enabling an iterative inference algorithm to augment the region of attraction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_12813 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Robustly Learning Regions of Attraction from Fixed Data Tacchi, Matteo Lian, Yingzhao Jones, Colin Optimization and Control While stability analysis is a mainstay for control science, especially computing regions of attraction of equilibrium points, until recently most stability analysis tools always required explicit knowledge of the model or a high-fidelity simulator representing the system at hand. In this work, a new data-driven Lyapunov analysis framework is proposed. Without using the model or its simulator, the proposed approach can learn a piece-wise affine Lyapunov function with a finite and fixed off-line dataset. The learnt Lyapunov function is robust to any dynamics that are consistent with the off-line dataset, and its computation is based on second order cone programming. Along with the development of the proposed scheme, a slight generalization of classical Lyapunov stability criteria is derived, enabling an iterative inference algorithm to augment the region of attraction. |
| title | Robustly Learning Regions of Attraction from Fixed Data |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2305.12813 |