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In this paper, the optimal topology structure is studied for hybrid-weighted leader-follower multiagent systems (MASs). The results are developed by taking advantage of linear quadratic regulator (LQR) theory. We show that the multiagent star composite structure is the optimal topology which can enable the MAS to achieve the bipartite consensus. In particular, we prove that the optimal topology corresponding to the multiagent system with the first-order static leader and the second-order dynamic leader is, respectively, a hybrid-weighted star composite structure and an unevenly hybrid-weighted star composite structure. The results of the paper indicate that, in addition to the necessary information communication between leader and followers, the information exchange among followers increases the control cost of the system.

LQR Based Optimal Topology of Hybrid-Weighted Multiagent Systems