The gray-box feedback optimization approach has a wide range of potential applications beyond the steady-state optimization discussed in the article. Some of these applications include:
Model Predictive Control (MPC): In MPC, the gray-box controller can be used to optimize control inputs over a finite time horizon based on a predictive model of the system. By incorporating real-time measurements and adaptive combination of model-based and model-free components, the gray-box controller can enhance the performance of MPC systems, especially in cases where accurate models are unavailable or uncertain.
Reinforcement Learning (RL): In RL, the gray-box controller can be utilized to optimize the policy of an agent interacting with an environment to maximize a cumulative reward. By integrating approximate sensitivities and gradient estimates, the gray-box approach can improve the sample efficiency and stability of RL algorithms, making them more robust to uncertainties and inaccuracies in the system dynamics.
Stochastic Optimization: The gray-box controller can also be applied to stochastic optimization problems where the objective function or constraints involve random variables. By adapting the controller's update rules to handle stochastic gradients or noisy measurements, the gray-box approach can effectively optimize under uncertainty and variability.
Adaptive Control: In adaptive control systems, the gray-box controller can be used to adjust control parameters based on real-time feedback and a combination of model-based and model-free updates. This adaptive approach allows the controller to adapt to changing system dynamics and disturbances, improving the robustness and performance of the control system.
Overall, the gray-box feedback optimization approach has versatile applications in various fields beyond steady-state optimization, offering benefits in terms of adaptability, robustness, and efficiency in optimizing complex systems.