Optimal topology for consensus of heterogeneous multi-agent systems

Consensus can be achieved under various topologies for multi-agent systems. Then, which one is the optimal? In this paper, we consider the problem of optimal topology for consensus of heterogeneous multi-agent systems. We assume that the system consists of a leader and several followers with heterogeneous dynamics. Firstly, we define a quadratic cost function composed of consensus error and control effort for the heterogeneous multi-agent system. Secondly, by using linear-quadratic regulator theory and matrix theory, we prove that the optimal position topology and the optimal velocity topology are star graphs. Finally, simulations are carried out to illustrate the effectiveness of the theoretical results.