Fully distributed scaled consensus tracking of high-order unknown nonlinear multi-agent systems

An adaptive fast robust scaled consensus tracking problem for multi-agent systems (MASs) with unknown dynamics is studied in this paper under a directed graph. Each agent's dynamic is described by a high-order differential equation, which includes time delays and uncertainty. A novel fully distributed adaptive control method is proposed to ensure that all following agents track the leader with prescribed scaled ratios asymptotically, and the tracking errors are uniform ultimate boundedness. Meantime the proposed approach guarantees the bounded adaptive estimates of the unknown parameters and dynamics, and can lighten the burden on computation because it only needs to update a small number of adaptive parameters. The control gain of each agent is heterogeneous and time-varying. It changes and updates by the designed distributed adaptive law. The presented protocol doesn't need to know global nonzero eigenvalues of communication graph adjacency matrix, and is independent of any global information. Finally, the effectiveness of the theoretical results is verified by a numerical example.