# Economically Efficient Combined Plant and Controller Design Using Batch Bayesian Optimization: Mathematical Framework and Airborne Wind Energy Case Study

## TL;DR

This paper introduces a data-driven nested optimization framework using Bayesian Optimization and Gaussian Processes to efficiently co-design plant and controller parameters, validated on an airborne wind energy case study.

## Contribution

It presents a novel Bayesian Optimization-based approach for coupled plant-controller design without requiring explicit system models, incorporating batch optimization for efficiency.

## Key findings

- Parameters converge within few iterations.
- Framework effectively handles systems without closed-form models.
- Validated on airborne wind energy system.

## 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.