Coordinated tracking in mean square for a multi-agent system with noise perturbations

In this paper, a coordinated tracking control problem for a multi-agent system under noise perturbations is considered over a leader-follower communication network. Two control gain functions are designed where the first one is used to attenuate the effect of noise and the second to stabilize the system. Using tools from the algebraic graph theory and stochastic analysis, it is proved that the followers can track the leader in mean square over a time-invariant network. The results are then extended to the scenario of a time-varying network.