Non-Fragility and Partial Controllability of Multi-Agent Systems

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

Controllability of Heterogeneous Multi-Agent Networks

The existing results on controllability of multi-agents networks are mostly based on homogeneous nodes. This paper focuses on controllability of heterogeneous multi-agent networks, where the agents are modeled as two types. One type is that the agents are of the same high-order dynamics, and the interconnection topologies of the information flow in different orders are supposed to be different. It is proved that a heterogeneous-topology network is controllable if and only if the first-order information topology is leader-follower connected, and there exists a Laplacian matrix, which is a linear combination of the Laplacian matrices of each order information, whose corresponding topology is controllable. The other type is that the agents are of generic linear dynamics, and the dynamics are supposed to be heterogeneous. A necessary and sufficient condition for controllability of heterogeneous-dynamic networks is that each agent contains a controllable dynamic part, and the interconnection topology of the network is leader-follower connected. If some dynamics of the agents are not controllable, the controllability between the agents and the whole network is also studied by introducing the concept of eigenvector-uncontrollable. Different illustrative examples are provided to demonstrate the effectiveness of the theoretical results in this paper