Real-time control using Bayesian optimization: A case study in airborne wind energy systems

This paper presents a framework by which a data-driven optimization technique known as Bayesian Optimization can be used for real-time optimal control. In particular, Bayesian Optimization is applied to the real-time altitude optimization of an Airborne Wind Energy (AWE) system, for the purpose of maximizing net energy production. Determining the optimal operating altitude of an AWE system is challenging, as the wind speed constantly varies with both time and altitude. Furthermore, without expensive auxiliary equipment, the wind speed is only measurable at the AWE system's operating altitude. In this work, Gaussian Process modeling and Bayesian Optimization are used in real-time to optimize the AWE system's operating altitude efficiently, without the use of auxiliary wind profiling equipment. Specifically, the underlying objective function is modeled by a Gaussian Process (GP); then, Bayesian Optimization utilizes the predictive uncertainty information from the GP to determine the best subsequent operating altitude. In the AWE application, context-dependent Bayesian Optimization is used to handle the time-varying nature of the wind shear profile (wind speed vs. altitude). Using real wind data, our method is validated against three baseline approaches. Our simulation results show that the Bayesian Optimization method is successful in significantly increasing power production over these baselines.