Decentralized adaptive consensus control of uncertain nonlinear systems under directed topologies

In this paper, a decentralized adaptive backstepping control strategy is presented to solve leaderless and leader-following consensus problems for the outputs of nonlinear multi-agent systems with arbitrary subsystem orders and parametric uncertainties. Suppose that the information exchange conditions among distinct subsystems in the entire group can be represented by a directed topology and the corresponding connectivity matrix is unknown to each subsystem. In contrast to most of the existing results, Lyapunov function is not defined directly based on local consensus errors in all subsystems with the output information of their neighbors involved. Thus the difficulties in treating coupled terms related to local consensus errors and other subsystems´ parameter estimation errors, which are resulted from asymmetric property of directed graph, can be overcome. It is shown that with our proposed strategy, all the closed-loop signals are ensured uniformly ultimately bounded and asymptotical consensus can be achieved.