publication . Preprint . Article . 2018

A measure theoretic approach to traffic flow optimization on networks

Simone, Cacace; Fabio, Camilli; Raul De Maio,; Tosin, Andrea;
Open Access English
  • Published: 02 Mar 2018
  • Country: Italy
Abstract
We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective isto minimise/maximise macroscopic quantities, such as traffic volume or average speed,controlling few agents, for example smart traffic lights and automated cars. The measuretheoretic approach allows to study in a same setting local and nonlocal drivers interactionsand to consider the control variables as additional measures interacting with the driversdistribution. We also propose a gradient descent adjoint-based optimization method, ob-tained by deriving first-order optimality conditions for the control p...
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free text keywords: Mathematics - Optimization and Control, Mathematics - Analysis of PDEs, 49J20, 35B37, 35R02, 49M07, 65M99, Network, transport equation, measure-valued solutions, transmission conditions, optimization
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