Well-posedness of networked scalar semilinear balance laws subject to nonlinear boundary control operators

Shuxia Tang, Alexander Keimer, Alexandre Bayen

Research output: Contribution to conferencePaper

Abstract

Networked scalar semilinear balance laws are used as simplified macroscopic vehicular traffic models. The related initial boundary value problem is investigated, on a finiteinterval. The upstream boundary datum is determined by anonlinear feedback control operator, representing the fact thattraffic routing might be influenced in real time by the trafficinformation on the entire network. The main contribution ofthe present work lies in the appropriate design of nonlinearboundary control operators which meanwhile guarantee thewell-posedness of the resultant systems. In detail, two differenttypes of specific nonlinear boundary control operators areinstantiated, one being Lipschitz continuous and taking intoaccount traffic information from initial time up to present time,one using only delayed traffic information. This contributionthus presents simplified road traffic network dynamics whererouting at intersections is dependent of the status of the entirenetwork, incorporating als
Original languageEnglish
StatePublished - Dec 11 2019

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