Minimum stopping distance for linear control of an automatic car-following system

Linearized longitudinal dynamics of an automatic car-following system are analyzed to determine the minimum headway required to avoid collisions. We determine the linear controller with multiple control factors that satisfy all of the system constraints and have a minimum stopping distance. The constraints are stability, no oscillations, and the control forces remaining within a specified physical limitation of the vehicle. Numerical results show that a linear controller that satisfies all of the system constraints requires a large headway in order to avoid collisions when subject to extreme initial conditions. The results indicate the need for a nonlinear controller if collisions are to be avoided with proposed small headways.