Design Convergence Using Stability Concepts from Dynamical Systems Theory
Bradley Steinfeldt, Robert D. Braun · 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference · 2012
The inherent iteration required in the multidisciplinary design problem allows the design problem to cast as a dynamical system. The iteration in design is a resultant of the two rootnding problems. The rst root-nding problem is in seeking out candidate designs while the second is in optimizing the candidate designs. Viewing the root-nding schema as a dynamical system allows the application of established techniques from dynamical systems theory to design. Stability theory is one of the techniques that is enabled by viewing multidisciplinary design as a dynamical system. Stability theory is capable of providing information on whether or not a design will converge for a given iteration scheme, starting values for the iteration that will lead to convergence, as well as information regarding how fast a design will converge. Following the theoretical development, each of these concepts is demonstrated on sample problems showing the benet of the application of stability theory in the design realm.