Title: Economically Efficient Combined Plant and Controller Design Using Batch Bayesian Optimization: Mathematical Framework and Airborne Wind Energy Case Study,
Abstract: We present a novel data-driven nested optimization framework that addresses
the problem of coupling between plant and controller optimization. This
optimization strategy is tailored towards instances where a closed-form
expression for the system dynamic response is unobtainable and simulations or
experiments are necessary. Specifically, Bayesian Optimization, which is a
data-driven technique for finding the optimum of an unknown and
expensive-to-evaluate objective function, is employed to solve a nested
optimization problem. 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 control or
plant parameters. The proposed framework differs from the majority of co-design
literature where there exists a closed-form model of the system dynamics.
Furthermore, we utilize the idea of Batch Bayesian Optimization at the plant
optimization level to generate a set of plant designs at each iteration of the
overall optimization process, recognizing that there will exist economies of
scale in running multiple experiments in each iteration of the plant design
process. We validate the proposed framework for a Buoyant Airborne Turbine
(BAT). We choose the horizontal stabilizer area, longitudinal center of mass
relative to center of buoyancy (plant parameters), and the pitch angle
set-point (controller parameter) as our decision variables. Our results
demonstrate that these plant and control parameters converge to their
respective optimal values within only a few iterations.