标题： 基于顺序反馈优化的风场控制应用 显示英文标题

标题： Sequential feedback optimization with application to wind farm control

摘要： 本文提出了一种顺序线性化反馈优化框架，用于将非线性动力系统引导至最优稳态。 反馈优化中的一个基本挑战是需要准确的一阶信息的稳态输入输出映射，这对于高维非线性系统来说计算上是不可行的，并且在固定工作点附近进行近似时通常会导致性能不佳。 为解决这一限制，我们提出了一种顺序算法，在优化过程中自适应地更新线性化点，从而在整个轨迹中保持局部准确性。 我们证明了收敛到最优稳态的邻域，并给出了明确的误差界。 为了减少重复线性化操作的计算负担，我们进一步开发了一个多时间尺度变体，其中线性化更新发生在比优化迭代更慢的时间尺度上，在保持收敛保证的同时实现了显著的计算节省。 通过一个现实的风电场控制问题的数值仿真，验证了所提出的框架的有效性。 结果验证了理论收敛预测以及我们多时间尺度公式的预期计算优势。 显示英文摘要

摘要： 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.