Output Bipartite Consensus for Second-Order Heterogeneous Uncertain Agents With State-Dependent Cooperation-Competition Interactions

For state-dependent cooperation-competition networks, the output bipartite consensus problem of heterogeneous uncertain agents is studied in this article. In our framework, all the agents are described by second-order continuous-time nonlinear systems with different intrinsic dynamics, and the agents' uncertainties are characterized by unknown parameters in the intrinsic term. Then, the edge evolution rules with hysteresis coefficients are proposed via the classification strategy. To solve this problem, the distributed Lyapunov-based redesign method with the potential function term is first applied to such a second-order heterogeneous uncertain multiagent system. Through the three-step correlation design, the explicit expressions of the distributed controllers and the unknown parameter estimators are obtained, and it is shown that the state-dependent cooperation-competition network is always connected and maintains structural balance for all time if an initial structurally balanced and connected network topology is provided. On this basis, it follows from the total Lyapunov function that output bipartite consensus can be achieved asymptotically for the heterogeneous uncertain multiagent system. Finally, a numerical simulation is provided to validate the structural balance of state-dependent networks and output bipartite consensus of heterogeneous uncertain agents.