An Investigation of Equilibrium Stability in Decentralized Design Using Nonlinear Control Theory

The focus of this paper is a theoretical study of the design of complex engineering systems. More particularly, this paper studies the stability of equilibriums in decentralized design environments. Indeed the decomposition and coordination of decisions in the design of complex engineering systems is a great challenge. Companies who design these systems routinely allocate design responsibility of the various subsystems and components to different people, teams or even suppliers. The mechanisms behind this network of decentralized design decisions create difficult management and coordination issues. However, developing efficient design processes is paramount, especially with market pressures and customer expectations. Standard techniques to modeling and solving decentralized design problems typically fail to understand the underlying dynamics of the decentralized processes and therefore result in suboptimal solutions. This paper aims to model and understand the mechanisms and dynamics behind a decentralized set of decisions within a complex design process. Complex systems that are multidisciplinary and highly nonlinear in nature are the primary focus of this paper. Therefore, techniques such as Response Surface Approximations and Game Theory are used to discuss and solve the issues related to multidisciplinary optimization, while techniques and knowledge from Nonlinear Control theory are used to discuss the stability of some equilibrium points. Illustrations of the results are provided in the form of the study of a decentralized design of a pressure vessel.