Learning Neural Controllers with Optimality and Stability Guarantees Using Input-Output Dissipativity
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909641599877120 |
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| author | Wang, Han Miao, Keyan Madeira, Diego Papachristodoulou, Antonis |
| author_facet | Wang, Han Miao, Keyan Madeira, Diego Papachristodoulou, Antonis |
| contents | Deep learning methods have demonstrated significant potential for addressing complex nonlinear control problems. For real-world safety-critical tasks, however, it is crucial to provide formal stability guarantees for the designed controllers. In this paper, we propose a new framework for designing neural controllers that achieve both stability and optimality with respect to certain functions. Our key idea is to exploit the concept of input-output dissipativity of nonlinear systems by learning neural storage functions and supply rate functions. As a generalization of Lyapunov theory, dissipativity theory provides a natural connection to optimal control theory, offering both stability guarantees and meaningful optimality certificates. The neural controllers can be directly derived from the learned supply rate functions and guarantee closed-loop stability while inheriting optimality properties that can be shaped towards user-defined control objectives. Extensive numerical experiments demonstrate the effectiveness of our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06564 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Neural Controllers with Optimality and Stability Guarantees Using Input-Output Dissipativity Wang, Han Miao, Keyan Madeira, Diego Papachristodoulou, Antonis Systems and Control Deep learning methods have demonstrated significant potential for addressing complex nonlinear control problems. For real-world safety-critical tasks, however, it is crucial to provide formal stability guarantees for the designed controllers. In this paper, we propose a new framework for designing neural controllers that achieve both stability and optimality with respect to certain functions. Our key idea is to exploit the concept of input-output dissipativity of nonlinear systems by learning neural storage functions and supply rate functions. As a generalization of Lyapunov theory, dissipativity theory provides a natural connection to optimal control theory, offering both stability guarantees and meaningful optimality certificates. The neural controllers can be directly derived from the learned supply rate functions and guarantee closed-loop stability while inheriting optimality properties that can be shaped towards user-defined control objectives. Extensive numerical experiments demonstrate the effectiveness of our approach. |
| title | Learning Neural Controllers with Optimality and Stability Guarantees Using Input-Output Dissipativity |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2506.06564 |