Interventional consensus for high-order multi-agent systems with unknown disturbances on coopetition networks

In this paper, an interventional consensus problem is formulated mathematically with signed graph theory and dynamical system theory. The interaction network associated with a multi-agent system is modeled by a signed graph (called coopetition network in sequel) and the dynamics of each agent is described by a high order differential equation with a nonlinear unknown time-varying disturbance. Then a distributed interaction law is designed for each agent to drive all agents belonging to two competitive subgroups to reach a bipartite consensus on a reference signal, which is generated by an exogenous system (called leader in sequel). Simultaneously, some neural network (NN) based adaptive estimators are proposed to estimate the nonlinear disturbances in the agent dynamics. The convergence of the bipartite consensus is analyzed by using a Lyapunov function method. Finally, some simulation results are presented to demonstrate the formation of the bipartite consensus.