On avoiding saturation in the control of vehicular platoons

We investigate some fundamental limitations and tradeoffs in the control of vehicular platoons. These systems are of considerable practical importance as they represent an example of systems on lattices in which different units are dynamically coupled only through feedback controls. We demonstrate that in very long platoons, to avoid large position, velocity, and control amplitudes, one needs to explicitly account for the initial deviations of vehicles from their desired trajectories. We further derive explicit constraints on feedback gains - for any given set of initial conditions - to achieve desired position transients without magnitude and rate saturation. 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.