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

TL;DR

The paper tackles the challenge of jointly optimizing plant design and controller performance for airborne wind energy systems when dynamics lack closed-form models. It introduces a data-driven nested co-design framework using Batch Bayesian Optimization with Gaussian Process surrogates and an Expected Improvement acquisition, enabling efficient exploration of expensive simulations or experiments. A key innovation is batch plant design via local penalization, plus continuous controller optimization mapped to simulation time windows, with a convergence criterion guiding termination. The Altaeros BAT case study demonstrates rapid convergence of both plant and controller parameters in only a few iterations and reveals clear economies of scale when employing batch evaluations, highlighting practical benefits for hardware-in-the-loop co-design and experimental campaigns.

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.

Figures (12)

• Figure 1: Altaeros Buoyant Airborne Turbine (BAT), Image Credit: altaeros
• Figure 2: Machine learning variant of nested plant and controller co-design using Batch Bayesian Optimization
• Figure 3: Clarification of iteration vs. time in the proposed framework
• Figure 4: Ground-fixed and body-fixed coordinates plus the key variables used in deriving Euler-Lagrangian dynamics.
• Figure 5: Block diagram of closed loop flight controller for the BAT. $z_{sp}$ denotes a constant altitude set-point. We choose $p_c = \theta_{sp}$ and $\textbf{p}_p =[x_{cm}-x_{cb} \ A_H]^T$ in our case study results.