Sequential feedback optimization with application to wind farm control

TL;DR

This paper introduces a sequential feedback optimization method that adaptively linearizes nonlinear systems to efficiently reach optimal steady states, demonstrated on wind farm control with proven convergence and computational benefits.

Contribution

It presents a novel sequential-linearization feedback optimization framework with a multi-timescale variant, improving efficiency and accuracy for high-dimensional nonlinear systems.

Findings

Proven convergence to a neighborhood of the optimal steady state.

Significant computational savings with the multi-timescale approach.

Validated effectiveness through wind farm control simulations.

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.