Prescribed Performance Control for Multi-Cluster Consensus using Matrix-Weighted Interactions

The paper focuses on distributed consensus control of multi-agent systems. In particular, we study prescribed performance control for a group of linear agents characterized by single integrator dynamics, interacting through a matrix-weighted graph topology. We design control laws to achieve multi-cluster consensus, where the final consensus states of individual clusters conform to a linear relationship among themselves. Our proposed control scheme ensures the confinement of errors between communicating agents within predefined limits. The conditions for the same are analytically proven. Furthermore, we substantiate our theoretical results using numerical simulations.