Effects of Graph Topology on Performance of Distributed Algorithms for Networked Control and Sensing

We consider distributed collaborative control and sensing as they frequently arise in networked control systems. The algorithms are constrained to use local information. We show by experiments that the performance of such distributed, local information based algorithms, can depend dramatically on the structure of the underlying topology (connectivity pattern) of the agents. We investigate the speed of convergence, accuracy, robustness and resiliency of such algorithms including consensus problems. We consider several graphs that can be used to represent collaborative control and communication patterns. We first show that small world topologies offer several advantages from a perspective of a favorable tradeoff between performance of collaborative behaviors vs costs of collaborative behaviors (or equivalently constraints for collaboration). Second, we show that a two level hierarchy consisting of carefully located and controlled ’leaders’ at the higher level and the rest of the agents at the lower level, can provide a very efficient communication pattern with substantial improvement of performance. We close with a description of the possible topologies for this two tier structure and their performance.