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This paper is concerned with the problem of adaptive bipartite tracking problem for multi-agent systems (MASs) over signed directed graphs with unknown nonlinear functions. Each following agent is modelled by a higher-order nonlinear system in nonstrict-feedback form. The virtual and the actual control items of the considered system are the power functions with positive odd integers rather than linear items. A distributed neural-based adaptive backstepping scheme is proposed, where the unknown nonlinear dynamics are approximated by Neural networks. Under the proposed protocol, the bipartite output tracking errors converge to a small neighbourhood of the origin and all the signals of the closed-loop system remain semiglobally uniformly ultimately bounded. Since the considered high-order non-strict feedback nonlinear MASs in our paper include some existing nonlinear MASs as the special case, our result can be extended to control more general nonlinear MASs. Finally, the simulation results illustrate the validity of the proposed schemes by a numerical example and a practical example about a group of forced damped pendulums.

Distributed adaptive bipartite consensus tracking of high-order nonstrict-feedback nonlinear multi-agent systems