Nonlinear Control for Multi-agent Formations with Delays in Noisy Environments

In this paper, we investigate the nonlinear control problem for multi-agent formations with communication delays in noisy environments and in directed interconnection topologies. A stable theory of stochastic delay differential equations is established and then some sufficient conditions are obtained based on this theory, which allow the required formations to be gained at exponentially converging speeds with probability one for time-invariant formations, time-varying formations, and time-varying formations for trajectory tracking under a special “multiple leaders” framework. Some numerical simulations are also given to illustrate the effectiveness of the theoretical results.