  Using a nonlocal second-order traffic flow model we present an approach to
control the dynamics towards a steady state. The system is controlled by the
leading vehicle driving at a prescribed velocity and also determines the steady
state. Thereby, we consider both, the microscopic and macroscopic scales. We
show that the fixed point of the microscopic traffic flow model is
asymptotically stable for any kernel function. Then, we present Lyapunov
functions for both, the microscopic and macroscopic scale, and compute the
explicit rates at which the vehicles influenced by the nonlocal term tend
towards the stationary solution. We obtain the stabilization effect for a
constant kernel function and arbitrary initial data or concave kernels and
monotone initial data. Numerical examples demonstrate the theoretical results.
