Adaptive Scaled Bipartite Consensus via Funnel Control

For consensus, one issue is that its various variants, such as group consensus, scaled consensus, and bipartite consensus, ought to be proposed as the expansion of research and applications. Another issue is that consensus should carry certain performance specifications, to meet some crucial demands, such as rapidity and safety. In this article, we investigate an integrated consensus (i.e., scaled plus bipartite consensus) with a prescribed convergence rate, for a class of uncertain nonlinear MASs. A funnel-based adaptive scheme is proposed for the scaled bipartite consensus. Specifically, a time-varying function is preselected to characterize the prescribed convergence rate. Utilizing this time-varying function and the relative states defined in the sense of the scaled bipartite consensus, a fully distributed protocol is designed. Therein, the funnel gains are critical ingredients to ensure the prescribed performance, since they would increase the control signal to be sufficiently large once the relative states approach the performance boundary. Particularly, the selected time-varying design function is added to act as a part of the control gain in the protocol, which is critical to forcing the ultimate convergence (to zero) of relative states. The proposed protocol is verified by a simulation example.