Equilibrium stability in decentralized design systems

Abstract

The focus of this paper is on complex systems, and it presents a theoretical study of the design of complex engineering systems. More particularly, this paper studies the stability of equilibria in decentralized design environments. Indeed, the decentralization of decisions is often recommended in the design of complex systems, and the decomposition and coordination of decisions are a great challenge. 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 modelling 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. Nonlinear control theory is used in this paper as a new approach to study the stability of equilibrium points of the design space. Illustrations of the results are provided in the form of the study of the decentralized design of a pressure vessel.

Keywords:

• Decentralized design
• Decomposition
• Game Theory
• Nash equilibrium
• Response surface
• Nonlinear control
• Lyapunov theory

Acknowledgements

We would first like to acknowledge Stephen Prajna for his help using the SOSTOOLS software to generate the Lyapunov function. We would also like to thank the National Science Foundation, grants DMII-9875706 (for the preliminary convergence work that led to this paper) and DMII-0322783 (for the stability work of this paper) for their support of this research.

Vincent Chanron received a Master of Science in aerospace engineering from the Ecole Nationale Supérieure d'Ingénieurs de Constructions Aéronautiques (ENSICA) in Toulouse (France) in 2002. He also received a Master of Science in mechanical engineering from the University at Buffalo in 2002. He is completing his Ph.D. in August 2005 and his dissertation focuses on the dynamics and convergence of decentralized design processes. Starting in September 2005, he will be working for Airbus in Hamburg, Germany on the research and development of vertical tail aircraft.

Tarunraj Singh received his B.E., M.E and Ph.D. degrees in mechanical engineering from Bangalore University, Indian Institute of Science and the University of Waterloo respectively. He was a post doctoral fellow in the Aerospace Engineering Dept. of Texas A & M University prior to starting his tenure at the University at Buffalo in 1993, where he is currently a Professor in the Department of Mechanical and Aerospace Engineering. He was a von Humboldt fellow and spent his sabbatical at the Technische Universität Darmstadt in Germany and at the IBM Almaden Research center in 2000–2001. He was a NASA Summer Faculty Fellow at the Goddard Space Flight Center in 2003. His research interests are in robust vibration control, optimal control, nonlinear estimation and intelligent transportation. His research is supported by the National Science Foundation, AFOSR, NSA, Office of Naval Research and various industries. He has published over 100 refereed journal and conference papers and has over 30 invited seminars at various universities and research laboratories.

Kemper Lewis received his B.A. in mathematics and B.S. in mechanical engineering from Duke University, and his M.S. and Ph.D. degrees in mechanical engineering from Georgia Institute of Technology. His tenure at the University at Buffalo began in 1996, where he is currently an Associate Professor in the Department of Mechanical and Aerospace Engineering. He is also Executive Director of the New York State Center for Engineering Design and Industrial Innovation (NYSCEDII). His research areas include design theory, distributed design, reconfigurable systems, multidisciplinary optimization, and multiobjective design. He has over 100 technical publications in these research areas. His awards include the Society of Automotive Engineers Teetor Award, the ASME Black and Decker Best Paper Award, the State University of New York Chancellor's Award for Excellence in Teaching, and the National Science Foundation Career Award.