Design Convergence Using Stability Concepts from Dynamical Systems Theory

摘要

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 root-finding problems. The first root-finding problem is in seeking out candidate designs while the second is in optimizing the candidate designs. Viewing the root-finding 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 benefit of the application of stability theory in the design realm.