Using Dynamical Systems Concepts in Multidisciplinary Design

Abstract

A general multidisciplinary design problem features coupling and feedback between contributing analyses. This feedback may lead to convergence issues requiring significant iteration to obtain a feasible design. This work casts the multidisciplinary design problem as a dynamical system to 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 evaluate the robustness of the multidisciplinary design. These three dynamical system techniques are then combined in a methodology for the rapid robust design of linear multidisciplinary systems. The developed robust design methodology allows for uncertainty within the models as well across the parameters of the multidisciplinary problem and shows extensibility to nonlinear systems. Although viewing the multidisciplinary design optimization problem as a dynamical system is natural for designs in which there are contributing analyses defined by dynamic equations, this approach is shown to be applicable to general problems where the contributing analysis output is algebraic. The applicability and performance of the developed technique is demonstrated through linear and nonlinear example problems.