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While integrated physical and control system co-design has been demonstrated successfully on several engineering system design applications, it has been primarily applied in a deterministic manner without considering uncertainties. An opportunity exists to study non-deterministic co-design strategies, taking into account various uncertainties in an integrated co-design framework. Reliability-based design optimization (RBDO) is one such method that can be used to ensure an optimized system design being obtained that satisfies all reliability constraints considering particular system uncertainties. While significant advancements have been made in co-design and RBDO separately, little is known about methods where reliability-based dynamic system design and control design optimization are considered jointly. In this article, a comparative study of the formulations and algorithms for reliability-based co-design is conducted, where the co-design problem is integrated with the RBDO framework to yield solutions consisting of an optimal system design and the corresponding control trajectory that satisfy all reliability constraints in the presence of parameter uncertainties. The presented study aims to lay the groundwork for the reliability-based co-design problem by providing a comparison of potential design formulations and problem–solving strategies. Specific problem formulations and probability analysis algorithms are compared using two numerical examples. In addition, the practical efficacy of the reliability-based co-design methodology is demonstrated via a horizontal-axis wind turbine structure and control design problem. 

Co-design, or integrated physical and control system design, has been demonstrated successfully for several engineering system design optimization applications, primarily in a deterministic manner. An opportunity exists to study non-deterministic co-design strategies, including incorporation of uncertainty-induced failures, into an integrated co-design framework. Reliability-based design optimization (RBDO) is one such method that can be used to increase the likelihood of having a feasible design that satisfies all reliability constraints. While significant recent advancements have been made in co-design and RBDO separately, limited work has been done where reliability-based dynamic system design and control design optimization are considered jointly. In this paper, the co-design problem is integrated with the RBDO framework to yield a system-optimal design and the corresponding control trajectory, which satisfy all reliability constraints in the presence of parameter variations. Different problem formulations and RBDO algorithms are compared through numerical examples. The design of a horizontal-axis wind turbine (HAWT) supported by a lattice tower (with parameter uncertainties) is presented to demonstrate the applicability of the proposed method.