Controllability of heterogeneous multiagent systems

The existing results on controllability of multiagent systems (MASs) are mostly based on homogeneous nodes. This paper focuses on controllability of heterogeneous MASs, where the agents are modeled as two types. One type is that the agents have the same high-order dynamics, and the interconnection topologies of the information flow in different orders are supposed to be different; the other type is that the agents have generic linear dynamics, and the dynamics are supposed to be heterogeneous. For the first type, the necessary and sufficient condition for controllability of heterogeneous-topology system is derived via combination of Laplacian matrices. For the second type, the contribution also has two parts. The first part supposes that the agents have the same dimensional states and proves that controllability of this kind of MASs is equivalent to the controllability of each node and the whole interconnection topology, while the last parameter of the state feedback vector must not be 0. The second part supposes that the agents may have different dimensional states. For this kind of systems, the concept of beta-controllability is proposed. The necessary and sufficient condition for beta-controllability of heterogeneous-dynamic systems is also derived and it is also proved that the feedback gain vectors have the effect to improve controllability. Different illustrative examples are provided to demonstrate the effectiveness of the theoretical results in this paper.