Enhanced Convergence in Distributed Design Processes

The focus of this paper is on studying the convergence properties of the solution process of decentralized or distributed subsystems, where each subsystem has its own design problem, including objective(s), constraints, and design variables. The challenging aspect of this type of problem comes in the coupling of the subsystems, which create complex research and implementation challenges in modeling and solving these types of problems. We focus on the dynamics of these distributed design problems and attempt to further the understanding of the fundamental mechanics behind these processes in order to support the decisions being made by a network of decision makers. In this work, the domain of attraction, or region where convergence to a stable equilibrium point is guaranteed, of a decentralized design process is studied. Two approaches based on concepts from nonlinear control theory are presented: the first determines the domain of attraction for a specified Lyapunov function and the second optimizes for a Lyapunov function which maximizes the domain of attraction. The two techniques are illustrated on a benchmark pressure vessel design problem.