1 research outputs found
Swarm Aggregation under Fading Attractions
Gradient descent methods have been widely used for organizing multi-agent
systems, in which they can provide decentralized control laws with provable
convergence. Often, the control laws are designed so that two neighboring
agents repel/attract each other at a short/long distance of separation. When
the interactions between neighboring agents are moreover nonfading, the
potential function from which they are derived is radially unbounded. Hence,
the LaSalle's principle is sufficient to establish the system convergence. This
paper investigates, in contrast, a more realistic scenario where interactions
between neighboring agents have fading attractions. In such setting, the
LaSalle type arguments may not be sufficient. To tackle the problem, we
introduce a class of partitions, termed dilute partitions, of formations which
cluster agents according to the inter- and intra-cluster interaction strengths.
We then apply dilute partitions to trajectories of formations generated by the
multi-agent system, and show that each of the trajectories remains bounded
along the evolution, and converges to the set of equilibria