Feedback control of scalar conservation laws with application to density control in freeways by means of variable speed limits. (July 2019)

• Record Type: Journal Article
• Authors: Karafyllis, Iasson; Papageorgiou, Markos
• Is Part Of: Automatica. Volume 105(2019)
• Page Start: 228
• Page End: 236
• Publication Date: 2019-07
• Subjects: Conservation laws -- Hyperbolic PDEs -- Feedback stabilization -- Traffic control; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2019.03.021
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: 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.