Design of engineering systems in general, and actively-controlled dynamic systems in particular benefits from the identification, modeling, and quantification of uncertainties that affect the performance of the system. Traditionally, such uncertainties are handled through methods available to each discipline. For example, in response to uncertainties, design engineers use methods such as robust design optimization (RDO) and reliability-based design optimization (RBDO), while control engineers use methods from robust and stochastic control theory. The integrated solution of uncertain dynamic systems through uncertain control co-design (UCCD), however, requires the development of novel methods that account for the bi-directional coupling between plant and control decisions. The first step is to define uncertainties and incorporate them into the UCCD problem formulation.

The implementation of such UCCD formulations with probabilistic uncertainties requires efficient uncertainty propagation techniques, such as generalized Polynomial Chaos, or simplified approximations (such as forst-order second moment) tailored for UCCD problem structure. For crisp or bounded uncertainties, worst-case or minimax robust formulation results in a nested problem structure, replacing the expensive uncertainty quantification with an optimization problem. The solution is often too conservative. One approach to address the conservativeness of the minimax robust solution is to use advanced control techniques such as the multi-stage, robust modep predicitve control.

Wave energy converters (WECs) are a promising candidate for meeting the increasing energy demands of today's society. However, its technology readiness level is still low compared to wind and solar technologies. Thus far, the primary focus in WEC literture has been on individual aspects of these complex devices, such as sizing, control, and layout, with only a few articles investigating the interaction among these domains. Potential improvements in WEC array performance may be realized by leveraging a system-level design framework that considers the entire device and its characteristic attributes, such as plant, control, and layout, concurrently. The goal of this project is to improve our understanding of such interactions and how it can be utilized to improve the energy generation of WEC farms and reduce its associated costs.

Several challenges exist in carrying out this investigation. Considering uncertainties from the wave resource (and other problem elements), appropriate uncertainty quantification methods are required. Estimation of hydrodynamic coefficients, which is often performed through boundary element methods, is computationally expensive. Therefore, advanced techniques such as many-body expansion, along with machine learning techniques (such as selective sampling through query by committee) need to be integrated in the design process. The resulting concurrent UCCD and layout optimization is highly complex and requires efficient non-gradient-based optimization algorithms.