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1. A Comparative Study of Formulations and Algorithms for Reliability-Based Co-Design Problems

   https://doi.org/10.1115/1.4045299  

   Cui, Tonghui; Allison, James T.; Wang, Pingfeng (March 2020, Journal of Mechanical Design)

   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. 

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2. Probabilistic Microgrid Energy Management with Interval Predictions

   https://doi.org/10.3390/en13123116  

   Cheng, Jiayu; Duan, Dongliang; Cheng, Xiang; Yang, Liuqing; Cui, Shuguang (June 2020, Energies)

   null (Ed.)

   In this paper, we consider a probabilistic microgrid dispatch problem where the predictions of the load and the Renewable Energy Source (RES) generation are given in the form of intervals. A hybrid method combining scenario-selected optimization and reserve strategy using the Model Predictive Control (MPC) framework is proposed. Specifically, first of all, an appropriate scenario is selected by the optimizer at each optimization stage, and then the optimal scheduling and reservation of system capacity are determined based on the selected scenario and possible variations in the future as provided by the predictors. In addition, a new reserve strategy is introduced to adaptively maintain system reliability and respond to variations in the hierarchical microgrid control. Simulations are conducted to compare our proposed method with the existing robust method and the deterministic dispatch with perfect information. Results show that our proposed method significantly improves the system efficiency while maintaining system reliability. 

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3. Machine learning enhanced control co-design optimization of an immersion cooled battery thermal management system

   https://doi.org/10.1063/5.0201438  

   Liu, Zheng; Kabirzadeh, Pouya; Wu, Hao; Fu, Wuchen; Qiu, Haoyun; Miljkovic, Nenad; Li, Yumeng; Wang, Pingfeng (July 2024, Journal of Applied Physics)

   The development of lithium-ion battery technology has ensured that battery thermal management systems are an essential component of the battery pack for next-generation energy storage systems. Using dielectric immersion cooling, researchers have demonstrated the ability to attain high heat transfer rates due to the direct contact between cells and the coolant. However, feedback control has not been widely applied to immersion cooling schemes. Furthermore, current research has not considered battery pack plant design when optimizing feedback control. Uncertainties are inherent in the cooling equipment, resulting in temperature and flow rate fluctuations. Hence, it is crucial to systematically consider these uncertainties during cooling system design to improve the performance and reliability of the battery pack. To fill this gap, we established a reliability-based control co-design optimization framework using machine learning for immersion cooled battery packs. We first developed an experimental setup for 21700 battery immersion cooling, and the experiment data were used to build a high-fidelity multiphysics finite element model. The model can precisely represent the electrical and thermal profile of the battery. We then developed surrogate models based on the finite element simulations in order to reduce computational cost. The reliability-based control co-design optimization was employed to find the best plant and control design for the cooling system, in which an outer optimization loop minimized the cooling system cost while an inner loop ensured battery pack reliability. Finally, an optimal cooling system design was obtained and validated, which showed a 90% saving in cooling system energy consumption. 

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4. An uncertainty-aware deep learning framework-based robust design optimization of metamaterial units

   https://doi.org/10.1007/s00158-025-03979-z  

   Wang, Zihan; Bhaduri, Anindya; Xu, Hongyi; Wang, Liping (March 2025, Structural and Multidisciplinary Optimization)

   Mechanical metamaterials represent an innovative class of artificial structures, distinguished by their extraordinary mechanical characteristics, which are beyond the scope of traditional natural materials. The use of deep generative models has become increasingly popular in the design of metamaterial units. The effectiveness of using deep generative models lies in their capacity to compress complex input data into a simplified, lower-dimensional latent space, while also enabling the creation of novel optimal designs through sampling within this space. However, the design process does not take into account the effect of model uncertainty due to data sparsity or the effect of input data uncertainty due to inherent randomness in the data. This might lead to the generation of undesirable structures with high sensitivity to the uncertainties in the system. To address this issue, a novel uncertainty-aware deep learning framework-based robust design approach is proposed for the design of metamaterial units with optimal target properties. The proposed approach utilizes the probabilistic nature of the deep learning framework and quantifies both aleatoric and epistemic uncertainties associated with surrogate-based design optimization. We demonstrate that the proposed design approach is capable of designing high-performance metamaterial units with high reliability. To showcase the effectiveness of the proposed design approach, a single-objective design optimization problem and a multi-objective design optimization problem are presented. The optimal robust designs obtained are validated by comparing them to the designs obtained from the topology optimization method as well as the designs obtained from a deterministic deep learning framework-based design optimization where none of the uncertainties in the system are explicitly considered. 

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5. Implicit Trajectory Planning for Feedback Linearizable Systems: A Time-varying Optimization Approach

   https://doi.org/10.23919/ACC45564.2020.9147997  

   Zheng, Tianqi; Simpson-Porco, John; Mallada, Enrique (July 2020, American Control Conference)

   We develop an optimization-based framework for joint real-time trajectory planning and feedback control of feedback-linearizable systems. To achieve this goal, we define a target trajectory as the optimal solution of a time-varying optimization problem. In general, however, such trajectory may not be feasible due to , e.g., nonholonomic constraints. To solve this problem, we design a control law that generates feasible trajectories that asymptotically converge to the target trajectory. More precisely, for systems that are (dynamic) full-state linearizable, the proposed control law implicitly transforms the nonlinear system into an optimization algorithm of sufficiently high order. We prove global exponential convergence to the target trajectory for both the optimization algorithm and the original system. We illustrate the effectiveness of our proposed method on multi-target or multi-agent tracking problems with constraints. 

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