{"ID":2839642,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.15588","arxiv_id":"2511.15588","title":"Real-Time Optimal Control via Transformer Networks and Bernstein Polynomials","abstract":"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.","short_abstract":"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 us...","url_abs":"https://arxiv.org/abs/2511.15588","url_pdf":"https://arxiv.org/pdf/2511.15588v1","authors":"[\"Gage MacLin\",\"Venanzio Cichella\",\"Andrew Patterson\",\"Irene Gregory\"]","published":"2025-11-19T16:19:12Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[\"Transformer\"]","has_code":false}