Sensitivity of Online Feedback Optimization to time-varying parameters
Marta Zagorowska, Lars Imsland
TL;DR
This paper addresses how Online Feedback Optimization (OFO) performance depends on algorithmic parameters and time-varying model mismatch. It derives closed-form sensitivity expressions by recasting the OFO update as a quadratic program and applying KKT-based differentiation, enabling exact assessment of how Φ responds to problem and OFO parameters, as well as to gradient mismatch. The authors validate the theory with a one-dimensional testbed and apply it to a gas-lift optimization, demonstrating time-dependent sensitivity where longer operation reduces the impact of single-step gradient errors and active constraints can induce discontinuities. The results offer a principled tool for tuning OFO parameters and assessing robustness to model mismatch, with practical implications for energy systems and other constrained control problems.
Abstract
Online Feedback Optimization uses optimization algorithms as dynamic systems to design optimal control inputs. The results obtained from Online Feedback Optimization depend on the setup of the chosen optimization algorithm. In this work we analyse the sensitivity of Online Feedback Optimization to the parameters of projected gradient descent as the algorithm of choice. We derive closed-form expressions for sensitivities of the objective function with respect to the parameters of the projected gradient and to time-varying model mismatch. The formulas are then used for analysis of model mismatch in a gas lift optimization problem. The results of the case study indicate that the sensitivity of Online Feedback Optimization to the model mismatch depends on how long the controller has been running, with decreasing sensitivity to mismatch in individual timesteps for long operation times.