Matrix-Scaled Consensus for Second-Order Uncertain Multi-Agent Systems Under a Directed Graph

In this paper, we propose a matrix-scaled consensus algorithm for second-order inertia uncertain multi-agent systems under a directed graph without using relative velocity information in multi-dimensional space. A proper reference model is designed for each agent to track and an adaptive control method is utilized to cancel the effect of parameter uncertainties. The agents asymptotically converge to different values depending on their scaling matrices, in which the final position of each agent is accurately calculated. We also give some simulation results to support our analysis.