Real-Time Optimal Control via Transformer Networks and Bernstein Polynomials
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909913674940416 |
|---|---|
| author | MacLin, Gage Cichella, Venanzio Patterson, Andrew Gregory, Irene |
| author_facet | MacLin, Gage Cichella, Venanzio Patterson, Andrew Gregory, Irene |
| contents | In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data generated by solving a sample of infinite- dimensional optimization problems using composite Bernstein collocation. Once trained, the Transformer efficiently generates near-optimal, feasible trajectories, making it well-suited for real-time applications. In motion planning for autonomous vehicles, for instance, these trajectories can serve to warm- start optimal motion planners or undergo rigorous evaluation to ensure safety. We demonstrate the effectiveness of this method through numerical results on a classical control problem and an online obstacle avoidance task. This data-driven approach offers a promising solution for real-time optimal control of nonlinear, nonconvex systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15588 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Real-Time Optimal Control via Transformer Networks and Bernstein Polynomials MacLin, Gage Cichella, Venanzio Patterson, Andrew Gregory, Irene Optimization and Control In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data generated by solving a sample of infinite- dimensional optimization problems using composite Bernstein collocation. Once trained, the Transformer efficiently generates near-optimal, feasible trajectories, making it well-suited for real-time applications. In motion planning for autonomous vehicles, for instance, these trajectories can serve to warm- start optimal motion planners or undergo rigorous evaluation to ensure safety. We demonstrate the effectiveness of this method through numerical results on a classical control problem and an online obstacle avoidance task. This data-driven approach offers a promising solution for real-time optimal control of nonlinear, nonconvex systems. |
| title | Real-Time Optimal Control via Transformer Networks and Bernstein Polynomials |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2511.15588 |