{"ID":2892695,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.15127","arxiv_id":"2507.15127","title":"Sequential feedback optimization with application to wind farm control","abstract":"This paper develops a sequential-linearization feedback optimization framework for driving nonlinear dynamical systems to an optimal steady state. A fundamental challenge in feedback optimization is the requirement of accurate first-order information of the steady-state input-output mapping, which is computationally prohibitive for high-dimensional nonlinear systems and often leads to poor performance when approximated around a fixed operating point. To address this limitation, we propose a sequential algorithm that adaptively updates the linearization point during optimization, maintaining local accuracy throughout the trajectory. We prove convergence to a neighborhood of the optimal steady state with explicit error bounds. To reduce the computational burden of repeated linearization operations, we further develop a multi-timescale variant where linearization updates occur at a slower timescale than optimization iterations, achieving significant computational savings while preserving convergence guarantees. The effectiveness of the proposed framework is demonstrated via numerical simulations of a realistic wind farm control problem. The results validate both the theoretical convergence predictions and the expected computational advantages of our multi-timescale formulation.","short_abstract":"This paper develops a sequential-linearization feedback optimization framework for driving nonlinear dynamical systems to an optimal steady state. A fundamental challenge in feedback optimization is the requirement of accurate first-order information of the steady-state input-output mapping, which is computationally pr...","url_abs":"https://arxiv.org/abs/2507.15127","url_pdf":"https://arxiv.org/pdf/2507.15127v1","authors":"[\"Shijie Huang\",\"Sergio Grammatico\"]","published":"2025-07-20T21:31:27Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}