Feedback Control of Scalar Conservation Laws with Application to Density Control in Freeways by Means of Variable Speed Limits
This work provides theoretical guarantees for density control in freeway traffic using variable speed limits, addressing a practical problem for traffic engineers.
The paper develops feedback control laws for stabilizing a uniform traffic density profile in a scalar conservation law model under variable speed limits, achieving global asymptotic stabilization with free inlet speed limits and regional exponential stabilization without them, while ensuring shock-free solutions.
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.