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Structural Balance Preserving and Bipartite Static Consensus of Heterogeneous Agents in Cooperation-Competition Networks

The structural balance preserving problem is studied in this article for heterogeneous agents in the state-dependent cooperation-competition network. The heterogeneous agents considered are described by second-order integrator systems with different intrinsic nonlinear dynamics, and velocity damping terms, and the initial network is structurally balanced, and connected, which can be divided into two cooperation subnetworks. To solve this problem, a novel classification strategy is applied, where two kinds of evolution rules among agents, and the distributed protocol based on a class of potential functions are proposed, respectively. Under this strategy, the heterogeneous multi-agent system can not only maintain the structural balance of cooperation-competition networks but also achieve bipartite static consensus. Finally, a numerical example is delivered to demonstrate the effectiveness of the theoretical analysis.