A measure theoretic approach to traffic flow optimization on networks

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Cacace, Simone; Camilli, Fabio; De Maio, Raul; Tosin, Andrea;
(2018)
  • Identifiers: doi: 10.1017/S0956792518000621
  • Subject: Mathematics - Optimization and Control | 49J20, 35B37, 35R02, 49M07, 65M99 | Mathematics - Analysis of PDEs

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, fo... View more
  • References (18)
    18 references, page 1 of 2

    1. L. Ambrosio, N. Gigli, G. Savare, Gradient ows in metric spaces and in the space of probability measures, Lectures in Mathematics ETH Zurich, Birkhauser Verlag, Basel, 2008.

    2. G. Albi, M. Bongini, E. Cristiani, D. Kalise, Invisible control of self-organizing agents leaving unknown environments, SIAM J. Appl. Math., 76 (2016), 1683-1710.

    3. N. Bellomo, B. Piccoli, A. Tosin, Modeling crowd dynamics from a complex system viewpoint, Math. Models Methods Appl. Sci., 22 (Supp. 2) (2012), 1230004.

    4. M. Bongini, G. Buttazzo, Optimal control problems in transport dynamics, Math. Models Methods Appl. Sci. 27 (2017), 427-451.

    5. A. Bressan, S. Canic, M. Garavello, M. Herty, B. Piccoli, Flows on networks: recent results and perspectives, EMS Surv. Math. Sci. 1 (2014), no. 1, 47-111.

    6. F. Camilli, R. De Maio, A. Tosin, Transport of measures on networks, Netw. Heterog. Media, 12 (2017), 191 - 215.

    7. F. Camilli, R. De Maio, A. Tosin, Measure-valued solutions to transport equations on networks with nonlocal velocity, J. Di erential Equations (in press) 2018.

    8. J. A. Can~izo, J. A. Carrillo, J. Rosado, A well-posedness theory in measures for some kinetic models of collective motion, Math. Models Methods Appl. Sci. 21 (2011), no. 3, 515-539.

    9. E. Cascetta, Transportation Systems Analysis, Springer, Heidelberg (2009).

    10. G.Cavagnari, A.Marigonda, B.Piccoli, Averaged time-optimal control problem in the space of positive Borel measures, Esaim COCV (2018), in press.

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