Consensus Seeking in Multi-vehicle Systems with a Time-varying Reference State

In this paper, we study the consensus problem in multi-vehicle systems where the information states of each vehicle approach a common time-varying reference state. We first analyze consensus algorithms with a constant reference state using graph theoretical tools. We then propose consensus algorithms with a time-varying reference state and show necessary and sufficient conditions under which consensus is reached on the time-varying reference state when only a portion of the vehicles (e.g., the unique team leader) have access to the reference state and those vehicles might not have directed paths to the other vehicles in the team. The reference state may be a time-varying exogenous signal or evolves according to a nonlinear model. These consensus algorithms are also extended to achieve relative state deviations between the vehicles.