Distributed Adaptive Consensus Output Tracking Problem of Nonlinear Multi-Agent Systems with Unknown High-Frequency Gain Signs under Directed Graphs

This paper deals with the consensus output tracking problem for multi-agent systems with unknown high-frequency gain signs, in which the subsystems are connected over directed graphs. The subsystems may have different dynamics, as long as the relative degrees are the same. A new type of Nussbaum gain is first presented to tackle adaptive consensus control of network-connected systems without the knowledge of the high-frequency gains. Adaptive laws and internal models are then proposed to handle the uncertainties and unknown parameters. An integral Lyapunov function based on sufficient conditions is finally introduced to tackle the asymmetry of the Laplacian matrix of directed graphs, into which we incorporate the new Nussbaum gain and the adaptive internal model to design the controller. It is apparent that the control scheme and the adaptive laws are fully distributed, which means that only the relative information of the neighbourhood subsystems' outputs is used, and the simulation results validate the effectiveness of the control design, whereby they guarantee the asymptotic convergence of errors to zero as well as the boundedness of the state variables.