Consensus of multi-agent directed networks with perturbations

In this paper, stochastic consensus seeking problem is considered for multi-agent networks on directed graphs with intrinsic deterministic nonlinear perturbations and stochastic noises. It is supposed that each agent can only use its local state and the state of its neighbors corrupted by white noises. Based on a transformation of matrix theory, the original stochastic system is turned into a reduced-order system. To attenuate the measurement noises, stochastic approximation type algorithm with decreasing step size is employed so that the individual states converge in mean square to the same limit. A sufficient criterion is obtained to guarantee mean square global asymptotical consensus of all agents. A simulation example is presented to illustrate the effectiveness of the proposed scheme.