Consensus Problem of Asymmetric Higher-Order Interaction Multi-agent Networks

This paper examines the consensus problem of multi-agent systems with asymmetric higher-order interactions amongst neighboring agents, where the asymmetric matrix-valued inter-agent coupling mechanism is employed to model the higher-order interactions amongst neighboring agents, and the associated pairwise interaction is also supposed to be irreciprocal. First, we reveal the fundamental mechanism of how asymmetric higher-order interactions influence the error elimination between a pair of neighboring agents according to the asymmetric/skew-symmetric decomposition of square matrices. Second, we provide sufficient conditions to guarantee the convergence of asymmetric HOI networks from the network topology perspective. By examining the null space of the Laplacian matrix associated with asymmetric HOI networks, we finally present necessary/sufficient conditions for achieving average consensus on asymmetric HOI networks.