Stability and safety of multi-vehicle systems

We study the safety control of multiple vehicles moving along a straight line. Each vehicle implements a linear feedback law on the positions and velocities of the adjacent vehicles. We assume the number of vehicles is large so by taking to the continuum limit the model is described by a hyperbolic partial differential equation, namely the wave equation. We analyze the stability of the system when each vehicle is subject to finite bandwidths of sensing and actuation. We also investigate the dynamic response of the system to disturbances. Finally, we specify the safety conditions of the system and safety control is formulated as a robust control problem.