Distributed methods for resource allocation - a passivity-based approach (2015)
Since the complexity and scale of systems have been growing in the last years, distributed approaches for control and decision making are becoming more prevalent. This dissertation focuses on an important problem involving distributed control and decision making, the dynamic resource allocation in a network. To address this problem, we explore a consensus?based algorithm that does not require any centralized computation, and that is capable to deal with applications modeled either by dynamical systems or by memoryless functions. The main contribution of our research is to prove, by means of graph theoretical tools and passivity analysis, that the proposed controller asymptotically reaches an optimal solution without the need of full information. In order to illustrate the relevance of our main result, we address several engineering applications including: distributed control for energy saving in smart buildings, management of the customers of an aggregating entity in a smart grid environment, and development of an exact distributed optimization method that deals with resource allocation problems subject to lower-bound constraints. Finally, we explore resource allocation techniques based on classic population dynamics models. In order to make them distributed, we introduce the concept of non-well-mixed population dynamics. We show that these dynamics are capable to deal with constrained information structures that are characterized by non-complete graphs. Although the proposed non-well-mixed population dynamics use partial information, they preserve similar properties of their classic counterpart, which uses full information. Specifically, we prove mass conservation and convergence to Nash equilibrium