Coordination of networked systems on digraphs with multiple leaders via pinning control

Abstract

It is well known that achieving consensus among a group of multi-vehicle systems by local distributed control is feasible if and only if all nodes in the communication digraph are reachable from a single (root) node. In this article, we take into account a more general case that the communication digraph of the networked multi-vehicle systems is weakly connected and has two or more zero-in-degree and strongly connected subgraphs, i.e. there are two or more leader groups. Based on the pinning control strategy, the feasibility problem of achieving second-order controlled consensus is studied. At first, a necessary and sufficient condition is given when the topology is fixed. Then the method to design the controller and the rule to choose the pinned vehicles are discussed. The proposed approach allows us to extend several existing results for undirected graphs to directed balanced graphs. A sufficient condition is proposed in the case where the coupling topology is variable. As an illustrative example, a second-order controlled consensus scheme is applied to coordinate the movement of networked multiple mobile robots.

Keywords:

• networked systems
• pinning control
• graphs
• consensus

Acknowledgements

This work was supported by the Specialised Research Fund for the Doctoral Programme of Higher Education SRFDP-09-0191120025 and the Innovation Ability Training Foundation of Chongqing University, by NSF grant ECCS-0801330, IIS-0326505, AFOSR grant FA9550-09-1-0278 and ARO grant W91NF-05-1-0314, CDJZR11170003.