Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2016, Article ID 2743251, 11 pages
http://dx.doi.org/10.1155/2016/2743251
Research Article

Exact Boundary Controllability for Free Traffic Flow with Lipschitz Continuous State

Department Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Cauerstraße 11, 91058 Erlangen, Germany

Received 3 December 2015; Accepted 21 March 2016

Academic Editor: Chaudry Masood Khalique

Copyright © 2016 Martin Gugat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. J. Lighthill and G. B. Whitham, “On Kinematic Waves. II. A theory of traffic flow on long crowded roads,” Proceedings of the Royal Society of London A, vol. 229, no. 1178, pp. 317–345, 1955. View at Publisher · View at Google Scholar
  2. P. I. Richards, “Shock waves on the highway,” Operations Research, vol. 4, pp. 42–51, 1956. View at Publisher · View at Google Scholar · View at MathSciNet
  3. R. M. Colombo and E. Rossi, “On the micro-macro limit in traffic flow,” Rendiconti del Seminario Matematico della Università Di Padova, vol. 131, pp. 217–235, 2014. View at Publisher · View at Google Scholar
  4. H. Greenberg, “An analysis of traffic flow,” Operations Research, vol. 7, pp. 79–85, 1959. View at Publisher · View at Google Scholar · View at MathSciNet
  5. R. F. Cunningham and C. F. White, “Vehicular tunnel traffic-flow control,” IEEE Transactions on Vehicular Technology, vol. 19, no. 1, pp. 120–127, 1970. View at Publisher · View at Google Scholar · View at Scopus
  6. C. A. Lave, “Speeding, coordination, and the 55 MPH limit,” The American Economic Review, vol. 75, no. 5, pp. 1159–1164, 1985. View at Google Scholar
  7. M. Quddus, “Exploring the relationship between average speed, speed variation, and accident rates using spatial statistical models and GIS,” Journal of Transportation Safety and Security, vol. 5, no. 1, pp. 27–45, 2013. View at Publisher · View at Google Scholar · View at Scopus
  8. T. Li, Controllability and Observability for Quasilinear Hyperbolic Systems, American Institute of Mathematical Sciences, Springfield, Ill, USA, 2010.
  9. M. Gugat, “Boundary controllability between sub- and supercritical flow,” SIAM Journal on Control and Optimization, vol. 42, no. 3, pp. 1056–1070, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. J.-M. Coron, O. Glass, and Z. Wang, “Exact boundary controllability for 1-D quasilinear hyperbolic systems with a vanishing characteristic speed,” SIAM Journal on Control and Optimization, vol. 48, no. 5, pp. 3105–3122, 2009/10. View at Publisher · View at Google Scholar · View at MathSciNet
  11. M. Gugat and G. Leugering, “Global boundary controllability of the de St. Venant equations between steady states,” Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol. 20, no. 1, pp. 1–11, 2003. View at Publisher · View at Google Scholar
  12. B. D. Greenshields, “A study of traffic capacity,” Proceedings of the Highway Research Record, vol. 14, pp. 448–477, 1935. View at Google Scholar
  13. M. Gugat, Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems, SpringerBriefs in Electrical and Computer Engineering, Birkhäuser, Basel, Switzerland, 2015.
  14. H. Zhang, S. G. Ritchie, and W. W. Recker, “Some general results on the optimal ramp control problem,” Transportation Research Part C, vol. 4, no. 2, pp. 51–69, 1996. View at Publisher · View at Google Scholar · View at Scopus
  15. D. Jacquet, C. C. De Wit, and D. Koenig, “Optimal ramp metering strategy with extended LWR model, analysis and computational methods,” in Proceedings of the 16th Triennial World Congress of International Federation of Automatic Control (IFAC '05), pp. 99–104, Prague, Czech Republic, July 2005. View at Scopus
  16. J. Reilly, S. Samaranayake, M.-L. Delle Monache, W. Krichene, P. Goatin, and A. M. Bayen, “Adjoint-based optimization on a network of discretized scalar conservation laws with applications to coordinated ramp metering,” Journal of Optimization Theory and Applications, vol. 167, no. 2, pp. 733–760, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. B. Seibold, M. R. Flynn, A. R. Kasimov, and R. R. Rosales, “Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models,” Networks and Heterogeneous Media, vol. 8, no. 3, pp. 745–772, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  18. B. Piccoli, K. Han, T. L. Friesz, T. Yao, and J. Tang, “Second-order models and traffic data from mobile sensors,” Transportation Research Part C, vol. 52, pp. 32–56, 2015. View at Publisher · View at Google Scholar · View at Scopus