Adaptive Consensualization for Lipschitz Nonlinear-type Multi-agent Networks with Fixed Topologies

Adaptive consensualization problems for Lipschitz nonlinear-type multi-agent networks with fixed topologies are addressed. By using the state errors of the neighboring agents, an adaptive consensus protocol is proposed to deal with the consensualization problems. To eliminate the impacts of the Lipschitz nonlinear dynamics, the structure property of a transformation matrix and the Laplacian matrix, and the Lipschitz condition are well utilized. In the Lyapunov function, a scaling constant is introduced to eliminate the impacts of eigenvalues of the Laplacian matrix, which are the global information of the whole multi-agent networks. Then, an completely distributed consensualization criterion is presented in terms of the linear matrix inequality. Furthermore, an explicit expression of the consensus function and its initial state of this multi-agent network are presented. In the Final, a numerical example is shown to verify the validity of theoretical results.