Utilizing Dynamical Systems Concepts in Multidisciplinary Design

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Steinfeldt, Bradley A.
Braun, Robert D.
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A general multidisciplinary design problem features coupling and feedback between contributing analyses. This feedback may lead to convergence issues requiring significant iteration in order to obtain a feasible design. This work provides a description for casting the multidisciplinary design problem as a dynamical system in order to overcome some of the challenges associated with traditional multidisciplinary design and leverage the benefits of dynamical systems theory in a new domain. Three areas from dynamical system theory are chosen for investigation: stability analysis, optimal control, and estimation theory. Stability analysis is used to investigate the existence of a solution to the design problem. Optimal control techniques allow the requirements associated with the design to be incorporated into the system and allow for constraints that are functions of both the contributing analysis outputs and input values to be handled simultaneously. Finally, estimation methods are employed to obtain an evaluation of the robustness of the multidisciplinary design. These three dynamical system techniques are then combined in a complete methodology for the rapid robust design of a linear multidisciplinary design. The developed robust design methodology allows for uncertainties both within the models as well as the parameters of the multidisciplinary problem. The performance of the developed technique is demonstrated through a linear and nonlinear example problem.
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