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We present a novel data-driven nested optimization framework that addressesthe problem of coupling between plant and controller optimization. Thisoptimization strategy is tailored towards instances where a closed-formexpression for the system dynamic response is unobtainable and simulations orexperiments are necessary. Specifically, Bayesian Optimization, which is adata-driven technique for finding the optimum of an unknown andexpensive-to-evaluate objective function, is employed to solve a nestedoptimization problem. The underlying objective function is modeled by aGaussian Process (GP); then, Bayesian Optimization utilizes the predictiveuncertainty information from the GP to determine the best subsequent control orplant parameters. The proposed framework differs from the majority of co-designliterature where there exists a closed-form model of the system dynamics.Furthermore, we utilize the idea of Batch Bayesian Optimization at the plantoptimization level to generate a set of plant designs at each iteration of theoverall optimization process, recognizing that there will exist economies ofscale in running multiple experiments in each iteration of the plant designprocess. We validate the proposed framework for a Buoyant Airborne Turbine(BAT). We choose the horizontal stabilizer area, longitudinal center of massrelative to center of buoyancy (plant parameters), and the pitch angleset-point (controller parameter) as our decision variables. Our resultsdemonstrate that these plant and control parameters converge to theirrespective optimal values within only a few iterations.

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