Formation control for nonlinear multi-agent systems with time-delay coupling and noise disturbance in directed graphs

In this paper, by using the stability theory of stochastic delay differential equations, we investigate a formation control problem of nonlinear multi-agent systems with time-delay coupling and noise disturbance under the assumption that the interconnection topology is a directed graph. Sufficient conditions are obtained for the attainment of both time-invariant and time-varying formations as well as for time-varying formations for trajectory tracking by using a special multiple leaders´ framework that attains the formations at exponentially converging speeds with a probability of one. Several numerical simulations are also given to illustrate the effectiveness of the theoretical results.