Second-order consensus for heterogeneous agents in the cooperation-competition network

In this paper, a second-order consensus problem is investigated for the heterogeneous agents in the cooperation-competition network, with the parameters of the agents dynamics being uncertain. By introducing an ex-osystem, a hybrid adaptive and pinning control strategy is firstly proposed to ensure that all the agents follow a desired trajectory which is a function of the exosystem state. Several effective sufficient conditions are obtained by applying algebraic graph theory and the Barbalat lemma. Besides, the switching topologies between the competition agents are also considered. With the help of the Barbalat-like lemma, it is found that second-order consensus problem of the heterogeneous agents can be solved even when the competition sub-network is dynamic. Finally, simulation result is presented to validate the effectiveness of the theoretical analysis.