Stochastic consensus in directed networks of agents with non-linear dynamics and repairable actuator failures

In this study, the problem of stochastic consensus in multi-agent systems of non-linear dynamical agents with state-dependent noise perturbations and repairable actuator failures is investigated. By appropriately constructing a Lyapunov function and using tools from the stochastic differential equations theory, it is proved that mean-square consensus in the closed-loop multi-agent systems with a fixed strongly connected topology can be achieved exponentially if the coupling strength of relative states among neighbouring agents is larger than a threshold value depending on the actuator failure rate. The convergence rate is also analytically given. The results are then extended to the more general case where the communication topology only contains a directed spanning tree. Numerical simulations are finally provided to illustrate the effectiveness of the theoretical analysis.