Leader selection and weight redesign problems for multi-agent systems.
Bin Zhao, Yongqiang Guan, Long Wang · arXiv (Cornell University) · 2015
For an uncontrollable system, adding leaders and adjusting edge weights are two methods to improve controllability. In this paper, controllability of multi-agent systems under directed topologies is studied, especially on leader selection problem and weight redesign problem. For the former one, necessary and sufficient algebraic conditions of single leader controllability are given. When a system cannot be controlled by only one leader, necessary and sufficient conditions for controllability with fewest leaders are proposed. To improve controllability by redesigning weights, the system is supposed to be structurally controllable, which holds if and only if the communication topology contains a spanning tree. It is proved that the number of fewest edges needed to adjust weights equals the rank deficiency of controllability matrix. An algorithm on how to perform weight redesign