Distributed multiple-bipartite consensus in networked Lagrangian systems with cooperative–competitive interactions

In combination with the collective behavior evolution of bipartite consensus and cluster/group consensus, this paper proposes notion multiple-bipartite in networked Lagrangian systems (NLSs), effectively integrating above emergent behaviors cooperative–competitive networks. The problems leaderless leader-following tracking are solved via deploying designed distributed adaptive torque controllers for uncertain NLSs. Compared traditional framework, antagonistic interactions can exist same subnetwork. By introducing an acyclic partition adding integral item control protocols, explicit expressions final states eventually obtained case. Moreover, case be realized finite time resorting to two predefined estimators embedded scheme. effectiveness scenarios has been illustrated through numerical simulations ten heterogeneous mechanical manipulators.