This paper presents a novel data-driven nested optimization framework that aims to solve the problem of coupling between plant and controller optimization. This optimization strategy is tailored towards instances where a closed-form expression for the system dynamics 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 the 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 decide 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. We validate the proposed framework for Altaeros’ Buoyant Airborne Turbine (BAT). We choose the horizontal stabilizer area and 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 plant and control parameters converge to optimal values within only a few iterations.

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This research presents an iterative framework for optimizing the plant and controller for complex systems by fusing expensive but valuable experiments with cheap yet less accurate simulations. At each iteration, G-optimal design is used to generate experiments and simulations within a prescribed design space that is shrunken in size after each successful iteration. The shrinking of the design space is determined through statistical characterization of a response surface model, and further shrinking is achieved at successive iterations through a numerical model correction factor that is driven by the results of experiments. An initial validation of this iterative design optimization framework was performed on an airborne wind energy (AWE) system, where tethers and an aerostat are used in place of a tower to elevate the turbine to high altitudes. Using a unique lab-scale setup for the experiments, the aforementioned iterative methodology was used to optimize the center of mass location and pitch angle set point for the airborne wind energy system. The optimum configuration yielded a substantial improvement in system responses as compared to a numerically optimized configuration. The framework was recently extended to include four variables (horizontal and vertical stabilizer areas, center of mass location, and pitch angle set point).

This paper presents and experimentally evaluates a nested combined plant and controller optimization (co-design) strategy that is applicable to complex systems that require extensive simulations or experiments to evaluate performance. The proposed implementation leverages principles from Gaussian Process (GP) modeling to simultaneously characterize performance and uncertainty over the design space within each loop of the co-design framework. Specifically, the outer loop uses a GP model and batch Bayesian optimization to generate a batch of candidate plant designs. The inner loop utilizes recursive GP modeling and a statistically-driven adaptation procedure to optimize control parameters for each candidate plant design in real time, during each experiment. The characterizations of uncertainty made available through the GP models are used to reduce both the plant and control parameter design space as the process proceeds, and the optimization process is terminated once sufficient design space reduction has been achieved. The process is validated in this work on a lab-scale experimental platform for characterizing the flight dynamics and control of an airborne wind energy (AWE) system. The proposed co-design process converges to a design space that is less than 8% of the original design space and results in more than a 50% increase in performance.