Consensus of second-order heterogeneous multi-agent systems under a directed graph

In this paper, we study the consensus problem for second-order heterogeneous multi-agent systems under a directed graph. Unlike the existing consensus algorithms for second-order multi-agent systems in which all agents are assumed to have common unit inertias or share common control gains, we allow the inertias and the control gains to be heterogeneous for each agent. Fully distributed consensus algorithms are proposed when there exist, respectively, absolute velocity damping and relative velocity damping. Moreover, an adaptive σ-modification scheme for the gain adaption is proposed, which renders smaller control gains and thus requires smaller amplitude on the control input without sacrificing the consensus convergence.