Yongqiang Guan

Bin Zhao, Yongqiang Guan, Long Wang

Controllability of multi-agent systems is determined by the interconnection topologies. In practice, losing agents can change the topologies of multi-agent systems, which may affect the controllability. This paper studies non-fragility of controllability influenced by losing agents. In virtue of the concept of cutsets, necessary and sufficient conditions are established from a graphic perspective, for strong non-fragility and weak non-fragility of controllability, respectively. For multi-agent systems which contain important agents, partial controllability is proposed in terms of the concept of controllable node groups, and necessary and sufficient criteria are established for partial controllability. Moreover, partial controllability preserving problem is proposed. Utilizing the concept of compressed graphs, this problem is transformed into finding the the minimal $\mathbf{\langle s,t\rangle}$ vertex cutsets of the interconnection graph, which has a polynomial-time complexity algorithm for the solution. Several constructive examples illuminate the theoretical results.

Bin Zhao, Yongqiang Guan, Long Wang

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 adjustment problem. For a given system, necessary and sufficient algebraic conditions for controllability with fewest leaders are proposed. From another perspective, when leaders are fixed, controllability could be improved by adjusting edge weights, and therefore the system is supposed to be structurally controllable, which holds if and only if the communication topology contains a spanning tree. It is also proved that the number of fewest edges needed to be assigned on new weights equals the rank deficiency of controllability matrix. An algorithm on how to perform weight adjustment is presented. Simulation examples are provided to illustrate the theoretical results.