Practical Bipartite Consensus for Networked Lagrangian Systems in Cooperation-Competition Networks

This paper gains an insight into the practical bipartite consensus problem of networked Lagrangian systems (NLSs) in the context of dynamics. The distributed leaderless and leader-following practical bipartite consensus control laws are proposed in cooperation-competition networks with uncertain parameters, effectively extending the theoretical framework in cooperation networks for NLSs. In the leaderless case, the symmetric regions are newly established to facilitate the final convergence analysis. By employing the structurally balanced networked topologies, a novel symmetric positive definite matrix is exploited to derive the gain selection criteria in the leader-following case. Finally, numerical simulations of a network of revolute joint manipulators are illustrated to verify the theoretical results under positive-negative and all-negative topologies.