Bipartite consensus of uncertain nonlinear multi-agent systems over cooperation-competition networks: a fully distributed NN adaptive control approach

Purpose Bipartite consensus problem for uncertain nonlinear multi-agent systems (MASs) under cooperation-competition networks is investigated in this paper. This paper aims to design a fully distributed continuous neural network (NN) adaptive control scheme under which asymptotical bipartite consensus can be achieved without requiring any global information. Design/methodology/approach First, an unknown input observer (UIO) is constructed based on relative outputs to estimate the relative full states among neighboring agents. Subsequently, two classes of NN adaptive controllers with fixed coupling strengths and dynamic coupling strengths are respectively proposed, in which a continuous term is designed by using the time varying boundary layer method to mitigate the effects of NN approximation errors. Findings By using Lyapunov stability theory, the authors demonstrate that asymptotical bipartite consensus can be achieved. In the scenario with fixed coupling strengths, consensus is ensured if the coupling strength exceed their respective positive lower bounds, which depend on eigenvalues of Laplacian matrix and upper bounds of NN approximation errors. In contrast, for the case with dynamic coupling strengths, asymptotical bipartite consensus can be reached in a fully distributed approach without requiring any global information such as Laplacian matrix and upper bounds of NN approximation errors. Originality/value Compared with existing works, the main contributions of this work are twofold: (I) asymptotical bipartite consensus can be achieved without relying on any global information, especially upper bounds of NN approximation errors. (II) Since NN approximation error is canceled by a smooth compensating term, chattering is avoided.