A hybrid framework for resource allocation among multiple agents moving on discrete environments

Abstract

AbstractWe consider the problem of controlling a multi‐agent system whose agents move across discrete locations. The agents attempt to extract resources from the environment while the environment, which may vary as the system evolves, distributes its resources according to the agents requests. The environment is modeled as a network of discrete nodes. Our ultimate goal is to design the dynamical policies that determine the behavior of agents and nodes, such that the usage of resources in the network is optimized. We propose a hybrid model to describe both agents and nodes. Several components of this model are design variables that may be obtained analytically. We then formulate an optimization problem that may be decomposed into two hierarchical optimization problems: an integer optimization problem that considers the distribution of agents among the nodes of the network; and a convex optimization problem within each node that corresponds to the distribution of resources of each node among its resident agents. We show that the optimization problem within each node is a special case of the formulation that models congestion control algorithms in the internet. We then use available results to solve a portion of the proposed hybrid description for agents and nodes. Moreover, we show that the resulting continuous dynamics are globally asymptotically stable, with their equilibrium point coinciding with the solution of the optimization problem. As a consequence, the proposed continuous dynamics yield an interconnected system that is stable on each possible configuration of agents and nodes. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society