Convergence and stability in distributed design of large systems

Decentralized systems constitute a special class of design under distributed environments. They are characterized as large and complex systems divided into several smaller entities that have autonomy in local optimization and decision-making. The mechanisms behind this network of decentralized design decisions create difficult management and coordination issues. 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. This paper builds on already existing results of convergence in decentralized design for simple problems to extend them to any kind of quadratic decentralized system. This involves two major steps: developing the convergence conditions for the distributed optimization problem, and finding the equilibrium points of the design space. Illustrations of the results are given in the form of hypothetical decentralized examples.