On the peaking phenomenon in the control of vehicular platoons

We investigate the peaking phenomenon in the control of large-scale vehicular platoons. These systems are of considerable practical importance as they represent an example of systems on lattices in which different subsystems are dynamically coupled only through feedback controls. We demonstrate that imposing a uniform rate of convergence for all vehicles towards their desired trajectories may generate large transient peaks in both velocity and control. We further derive explicit constraints on feedback gains-for any given set of initial conditions-to achieve desired position transients without magnitude and rate peaking. These constraints are used to generate the trajectories around which the states of the platoon system are driven towards their desired values without the excessive use of control effort. All results are illustrated using computer simulations of platoons containing a large number of vehicles.