Theoretical Analysis of Flocking Algorithms in Networks of Second Order Dynamic Agents With Switching Topologies

Abstract

This paper deals with a refined analysis and modification of existing results on the flocking algorithms proposed for the second order dynamic agents. In the present work, the limiting condition of ever connectivity is removed and it is proved that the flocking can be reached if only the union of the network proximity graphs during nonoverlapping time intervals becomes connected frequently enough. Also, it is proved that including a static virtual leader cannot model the group objective of achieving the desired velocity and it will stop eventually at a predefined point in the space. The convergence rate to this fixed point is determined too. The last contribution of this paper is definition of group configuration when only a fraction of agents are informed about the virtual leader.