Neural Controller for Incremental Stability of Unknown Continuous-time Systems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| author | Basu, Ahan Dey, Bhabani Shankar Jagtap, Pushpak |
| author_facet | Basu, Ahan Dey, Bhabani Shankar Jagtap, Pushpak |
| contents | This work primarily focuses on synthesizing a controller that guarantees an unknown continuous-time system to be incrementally input-to-state stable ($δ$-ISS). In this context, the notion of $δ$-ISS control Lyapunov function ($δ$-ISS-CLF) for the continuous-time system is introduced. Combined with the controller, the $δ$-ISS-CLF guarantees that the system is incrementally stable. As the paper deals with unknown dynamical systems, the controller as well as the $δ$-ISS-CLF are parametrized using neural networks. The data set used to train the neural networks is generated from the state space of the system by proper sampling. Now, to give a formal guarantee that the controller makes the system incrementally stable, we develop a validity condition by having some Lipschitz continuity assumptions and incorporate the condition into the training framework to ensure a provable correctness guarantee at the end of the training process. Finally, we demonstrate the effectiveness of the proposed approach through several case studies: a scalar system with a non-affine, non-polynomial structure, a one-link manipulator system, a nonlinear Moore-Greitzer model of a jet engine, a magnetic levitator system and a rotating rigid spacecraft model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18330 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Neural Controller for Incremental Stability of Unknown Continuous-time Systems Basu, Ahan Dey, Bhabani Shankar Jagtap, Pushpak Systems and Control This work primarily focuses on synthesizing a controller that guarantees an unknown continuous-time system to be incrementally input-to-state stable ($δ$-ISS). In this context, the notion of $δ$-ISS control Lyapunov function ($δ$-ISS-CLF) for the continuous-time system is introduced. Combined with the controller, the $δ$-ISS-CLF guarantees that the system is incrementally stable. As the paper deals with unknown dynamical systems, the controller as well as the $δ$-ISS-CLF are parametrized using neural networks. The data set used to train the neural networks is generated from the state space of the system by proper sampling. Now, to give a formal guarantee that the controller makes the system incrementally stable, we develop a validity condition by having some Lipschitz continuity assumptions and incorporate the condition into the training framework to ensure a provable correctness guarantee at the end of the training process. Finally, we demonstrate the effectiveness of the proposed approach through several case studies: a scalar system with a non-affine, non-polynomial structure, a one-link manipulator system, a nonlinear Moore-Greitzer model of a jet engine, a magnetic levitator system and a rotating rigid spacecraft model. |
| title | Neural Controller for Incremental Stability of Unknown Continuous-time Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2504.18330 |