Lyapunov-based Adaptive Transformer (LyAT) for Control of Stochastic Nonlinear Systems
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911325423140864 |
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| author | Akbari, Saiedeh Shen, Xuehui Xue, Wenqian Insinger, Jordan C. Dixon, Warren E. |
| author_facet | Akbari, Saiedeh Shen, Xuehui Xue, Wenqian Insinger, Jordan C. Dixon, Warren E. |
| contents | This paper presents a novel Lyapunov-based Adaptive Transformer (LyAT) controller for stochastic nonlinear systems. While transformers have shown promise in various control applications due to sequential modeling through self-attention mechanisms, they have not been used within adaptive control architectures that provide stability guarantees. Existing transformer-based approaches for control rely on offline training with fixed weights, resulting in open-loop implementations that lack real-time adaptation capabilities and stability assurances. To address these limitations, a continuous LyAT controller is developed that adaptively estimates drift and diffusion uncertainties in stochastic dynamical systems without requiring offline pre-training. A key innovation is the analytically derived adaptation law constructed from a Lyapunov-based stability analysis, which enables real-time weight updates while guaranteeing probabilistic uniform ultimate boundedness of tracking and parameter estimation errors. Experimental validation on a quadrotor demonstrates the performance of the developed controller. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15996 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lyapunov-based Adaptive Transformer (LyAT) for Control of Stochastic Nonlinear Systems Akbari, Saiedeh Shen, Xuehui Xue, Wenqian Insinger, Jordan C. Dixon, Warren E. Systems and Control This paper presents a novel Lyapunov-based Adaptive Transformer (LyAT) controller for stochastic nonlinear systems. While transformers have shown promise in various control applications due to sequential modeling through self-attention mechanisms, they have not been used within adaptive control architectures that provide stability guarantees. Existing transformer-based approaches for control rely on offline training with fixed weights, resulting in open-loop implementations that lack real-time adaptation capabilities and stability assurances. To address these limitations, a continuous LyAT controller is developed that adaptively estimates drift and diffusion uncertainties in stochastic dynamical systems without requiring offline pre-training. A key innovation is the analytically derived adaptation law constructed from a Lyapunov-based stability analysis, which enables real-time weight updates while guaranteeing probabilistic uniform ultimate boundedness of tracking and parameter estimation errors. Experimental validation on a quadrotor demonstrates the performance of the developed controller. |
| title | Lyapunov-based Adaptive Transformer (LyAT) for Control of Stochastic Nonlinear Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2512.15996 |