  The paper provides results for the stabilization of a spatially uniform
equilibrium profile for a scalar conservation law that arises in the study of
traffic dynamics under variable speed limit control. Two different control
problems are studied: the problem with free speed limits at the inlet and the
problem with no speed limits at the inlet. Explicit formulas are provided for
respective feedback laws that guarantee stabilization of the desired
equilibrium profile. For the first problem, global asymptotic stabilization is
achieved; while for the second problem, regional exponential stabilization is
achieved. Moreover, the solutions for the corresponding closed-loop systems are
guaranteed to be classical solutions, i.e., there are no shocks. The obtained
results are illustrated by means of a numerical example.

Optimization and Control;Systems and Control;Analysis of PDEs