Fully distributed observer-based protocols for bipartite consensus of directed nonlinear multi-agent systems: A proportional-integral-gain perspective

This paper presents a novel perspective on fully distributed adaptive protocol design for bipartite consensus under directed communication graphs. It is revealed that the fully distributed protocol is indeed a PI-gain design approach. Based on such PI-gain method, fully distributed observer-based protocols are proposed to solve the consensus problem of nonlinear multi-agent systems over directed cooperative-antagonistic networks, where the neural network approximation is introduced to tackle the unknown nonlinearity. Fully distributed continuous protocols are further presented by modifying the sign function with a decaying variable, which takes the advantage of avoiding chattering problem. Theoretical analysis and numerical simulations are given to support our main results.