Leaderless cluster consensus of second-order general nonlinear multiagent systems under directed topology

This paper studies the problem of leaderless CC (cluster consensus) for second-order MAS (multi-agent systems) with inherent nonlinearity under directed topology. Interactions among agents in each cluster are cooperative, but interactions between agents in different clusters can be cooperative or antagonistic. Also, there is a directed spanning tree in each subdigraph formed by interactions among agents within each cluster. Based on a reference model taking the relative error with respect to the original system states as an input, an adaptive CC protocol is designed under general inter-cluster couplings. A variable transformation is applied to transform the CC problem into a stability problem, and some sufficient conditions for CC are derived. Since these conditions are expressed as logarithmic norm inequalities of reduced-order matrices, they are easy to verify. Furthermore, when there are no nonlinear functions, a corollary of our main results is provided to substantially improve some existing results on the leaderless CC problem. Additionally, by introducing a fully distributed adaptive observer, a fully distributed adaptive CC protocol is devised for second-order general nonlinear MAS without leaders. Finally, the usefulness of the derived results is validated by illustrative examples.