Group consensus for heterogeneous multi-agent systems with parametric uncertainties

In this paper, a group consensus problem is investigated for the heterogeneous agents that are governed by the Euler–Lagrange system and the double-integrator system, respectively, and the parameters of the Euler–Lagrange system are uncertain. To achieve group consensus, a novel group consensus protocol and a time-varying estimator of the uncertain parameters are proposed. By combining algebraic graph theory with the Barbalat lemma, several effective sufficient conditions are obtained. It is found that the time-delay group consensus can be achieved provided that the inner coupling matrices are equal in the different sub-networks. Besides, the switching topologies between homogeneous agents are also considered, with the help of the Barbalat-like lemma, and some relevant results are also obtained. Finally, these theoretical results are demonstrated by the numerical simulations.