Efficient and Robust Communication Topologies for Distributed Decision Making in Networked Systems

J.S. Baras and P. Hovareshti

To appear in the Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, China, December 16 - 18, 2009.

Abstract

Distributed decision making in networked systems depends critically on the timely availability of critical fresh information. Performance of networked systems, from the perspective of achieving goals and objectives in a timely and efficient manner is constrained by their collaboration and communication structures (they are not necessarily the same) and their interplay with the networked system’s dynamics. Thus autonomous agents are critically influenced by their understanding of the network communication topology. We describe efficient communication topologies for distributed decision making and relate them to small world graphs and more generally to expander graphs. In most cases achieving the system objectives requires many agent to agent communications. A reasonable measure for system robustness to communication topology change is the number of spanning trees in the graph abstraction of the communication system. Solutions to this problem have also applications in trust and the relationship of trust to control. We address the problem of network formation with robustness and connectivity constraints. We show that the general combinatorial problem can be relaxed to a convex optimization problem. We solve the special case of adding a shortcut to a ring and provide insights for derivation of heuristics for the general case. We also analyze the small world effect in the context of abrupt increases in the number of spanning trees as a result of adding a few shortcuts to a base lattice in the Watts-Strogatz framework. Finally we describe generalizations to expander graphs.