A study on minimum time regulation of a bounded congested road with upstream flow control

Shuxia Tang, Alexander Keimer, Paola Goatin, Alexandre Bayen

Research output: Contribution to conferencePaperpeer-review

Abstract

This article is motivated by the practical problem of controlling traffic flow by imposing restrictive boundary conditions. For a one-dimensional congested road segment, we study the minimum time control problem of how to control the upstream vehicular flow appropriately to regulate the downstream traffic into a desired (constant) free flow state in minimum time. We consider the Initial-Boundary Value Problem (IBVP) for a scalar nonlinear conservation law, associatedto the Lighthill-Whitham-Richards (LWR) Partial Differential Equation (PDE), where the left boundary condition, also treatedas a valve for the traffic flow from the upstream, serves asa control. Besides, we set absorbing downstream boundaryconditions. We prove first a comparison principle for thesolutions of the considered IBVP, subject to comparable initial,left and right boundary data, which provides estimates on theminimal time required to control the system. Then we considera (sub-) optimal control problem and we give
Original languageEnglish
StatePublished - Dec 11 2019

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