Sensitivity of Online Feedback Optimization to time-varying parameters

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.