Second-order Consensus Algorithm with Extensions to Switching Topologies and Reference Models

In this paper, we extend the consensus algorithm for double integrator dynamics to the case that the information exchange topologies switch randomly with time and to the case that the final consensus value evolves according to a given nonlinear reference model. We show sufficient conditions under which consensus is reached under switching directed information exchange topologies. Unlike the consensus algorithm for single integrator dynamics, more stringent conditions are required to guarantee consensus under switching directed topologies in the case of the consensus algorithm for double integrator dynamics. In addition, we propose consensus algorithms so that the information variables of each vehicle approach the solution of a nonlinear reference model when only a portion of the vehicles in the team have access to the model.