Synchronization on the N-torus with noisy measurements

We consider the problem of cooperative control of unmanned vehicles in an uncertain environment in which each vehicle can obtain only noisy measurements of the other vehicles. In particular, we want to establish convergence to a de sired formation using a stochastic algorithm with measurement errors. In this paper, the problem of stabilization of parallel formations in a self-propelled particle model is considered, which can be modeled as synchronization on the N-torus in the presence of noisy measurements of relative phase. Simulations are included to illustrate the result.