Guaranteed bounds for traffic flow parameters estimation using mixed lagrangian - Eulerian sensing

46th Annual Allerton Conference on Communication, Control, and Computing

Volumn , Issue , 2008, Pages 636-645

  Claudel, Christian G ^a   Bayen, Alexandre M ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Berkeley   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DATA ASSIMILATIONS; EULERIAN; GUARANTEED BOUNDS; HAMILTON-JACOBI EQUATIONS; HOPF FORMULAS; LAGRANGIAN; LAGRANGIAN MEASUREMENTS; LINEAR PROGRAMS; MIXED BOUNDARIES; SUFFICIENT CONDITIONS; SYSTEM OF LINEAR INEQUALITIES; TRAFFIC DATUM; TRAFFIC FLOWS; TRAVEL TIME FUNCTIONS; UPPER AND LOWER BOUNDS; VIABILITY THEORIES; WELL-POSEDNESS;

CONTROL THEORY; CONVEX OPTIMIZATION; LAGRANGE MULTIPLIERS; PARAMETER ESTIMATION; TRAFFIC CONTROL;

TRAFFIC SURVEYS;

EID: 64549090035     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ALLERTON.2008.4797618     Document Type: Conference Paper

References (40)

1. J.-P. AUBIN. Viability Theory. Systems and Control: Foundations and Applications. Birkhäuser, Boston, MA, 1991.
2. J.-P. AUBIN. Viability kernels and capture basins of sets under differential inclusions. SIAM Journal on Control and Optimization, 40:853-881, 2001.
3. J.-P. AUBIN, A. M. BAYEN, and P. SAINT- PIERRE. Dirichlet problems for some Hamilton-Jacobi equations with inequality constraints. In press: SIAM Journal on Control and Optimization, 2008.
4. J.-P. AUBIN and H FRANKOWSKA. Set Valued Analysis. Systems and Control: Foundations and Applications. Birkhäuser, Boston, MA, 1990.
5. J. P. AUBIN, J. LYGEROS, M. QUINCAMPOIX, S. SASTRY, and N. SEUBE. Impulse differential inclusions: a viability approach to hybrid systems. IEEE Transactions on Automatic Control, 47 (1) :2-20, 2002.
6. A. AW and M. RASCLE. Resurrection of "second order" models of traffic flow. SIAM Journal of Applied Mathematics, 60 (3) :916-938, 2000.
7. E. N. BARRON and R. JENSEN. Semicontinuous viscosity solutions for Hamilton-Jacobi equations with convex Hamiltonians. Communications in Partial Differential Equations, 15:1713-1742, 1990.
8. A. BAYEN AND C. CLAUDEL AND P. SAINT- PIERRE. Computations of solutions to a class of Hamilton-Jacobi equations under viability constraints. pages 4737-4742, Dec. 2007.
9. S. BOYD and L. VANDENBERGHE. Convex Optimization. Cambridge University Press, Cambridge, U. K., 2004.
10. C. G. CLAUDEL and A. M. BAYEN. Lax-Hopf based incorporation of internal boundary conditions into Hamilton-Jacobi equation. Part I: theory. Submitted to IEEE Transactions on Automatic Control, 2008.
11. C. G. CLAUDEL and A. M. BAYEN. Lax-Hopf based incorporation of internal boundary conditions into Hamilton-Jacobi equation. Part II: Computational methods. Submitted to IEEE Transactions on Automatic Control, 2008.
12. C. G. CLAUDEL and A. M. BAYEN. Solutions to switched Hamilton-Jacobi equations and conservation laws using hybrid components. In M. Egerstedt and B. Mishra, editors, Hybrid Systems: Computation and Control, number 4981 in Lecture Notes in Computer Science, pages 101-115. Springer Verlag, 2008.
13. M. G. CRANDALL, L. C. EVANS, and P.-L. LIONS. Some properties of viscosity solutions of Hamilton-Jacobi equations. Transactions of the American Mathematical Society, 282 (2) :487-502, 1984.
14. M. G. CRANDALL and P.-L. LIONS. Viscosity solutions of Hamilton-Jacobi equations. Transactions of the American Mathematical Society, 277 (1) :1-42, 1983.
15. C. F. DAGANZO. A variational formulation of kinematic waves: basic theory and complex boundary conditions. Transporation Research B, 39B (2) :187-196, 2005.
16. C. F. DAGANZO. On the variational theory of traffic flow: well-posedness, duality and applications. Networks and heterogeneous media, 1:601-619, 2006.
17. th World congress on ITS, New York, N. Y., November 16-20 2008. Intelligent Transport Systems.
18. H. FRANKOWSKA. Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations. SIAM Journal of Control and Optimization, 31 (1) :257-272, 1993.
19. M. GARAVELLO and B. PICCOLLI. Traffic flow on networks. American Institute of Mathematical Sciences, 2006.
20. M. GRANT, S. BOYD, and Y. YE. CVX: Matlab Software for Disciplined Convex Programming. available at http://www.stanford. edu/boyd/cvx.
21. Z. HAN and B. H. KROGH. Reachability analysis of large-scale affine systems using low-dimensional polytopes. In Hybrid Systems: Computation and Control, number 3927 in Lecture Notes in Computer Science, pages 287-301. Springer Verlag, 2006.
22. th TRB Annual Meeting Compendium of Papers DVD, Washington D. C., January 13-17 2008. Transportation Research Board.
23. B. HOH, M. GRUTESER, R. HERRING, J. BAN, D. WORK, J. C. HERRERA, A. M. BAYEN, M. ANNAVARAM, and Q. JACOBSON. Virtual trip lines for distributed privacy-preserving traffic monitoring. to appear, MobiSys 2008, Breckenridge, CO.
24. R. ISAACS. Differential Games. Dover (reprint from John Wiley), New York, NY, 1999 (1965).
25. Y. ISHIKAWA, T. AWAJI, K. AKITOMO, and B. QIU. Successive correction of the mean sea surface height by the simultaneous assimilation of drifting buoy and altimetric data. Journal of Physical Oceanography, 26 (11) :2381-2397, 1996.
26. Z. JIA, C. CHEN, B. COIFMAN, and P. VARAIYA. The PeMS algorithms for accurate, real time estimates of g-factors and speeds from single loop detectors. In IEEE Intelligent Transportation Systems Conference Proceedings, pages 536-541, Oakland, CA, Aug. 2001.
27. R. J. LEVEQUE. Numerical Methods for Conservation Laws. Birkhäuser-Verlag, Basel, 1992.
28. 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, 229 (1178) :317-345, 1956.
29. Y. MAKIGAMI, G. F. NEWELL, and R. ROTHERY. Three-dimensional representation of traffic flow. Transportation Science, 5 (3) :303-313, Aug. 1971.
30. I. MITCHELL, A M. BAYEN, and C. J. TOMLIN. A time-dependent hamilton-jacobi formulation of reachable sets for continuous dynamic games. To appear, IEEE Transactions on Automatic Control, 2005.
31. K. MOSKOWITZ. Discussion of 'freeway level of service as influenced by volume and capacity characteristics' by D. R. Drew and C. J. Keese. Highway Research Record, 99:43-44, 1965.
32. G. F. NEWELL. A simplified theory of kinematic waves in highway traffic, Part (I), (II) and (III). Transporation Research B, 27B (4) :281-313, 1993.
33. C. PANICONI, M. MARROCU, M. PUTTI, and M. VERBUNT. Newtonian nudging for a Richards equation-based distributed hydrological model. Advances in Water Resources, 26 (2) :161-178, 2003.
34. S. PRAJNA, A. JADBABAIE, and G. J. PAPPAS. A framework for worst-case and stochastic safety verification using barrier certificates. IEEE Transactions on Automatic Control, 52 (8) :1415-1428, 2007.
35. P. I. RICHARDS. Shock waves on the highway. Operations Research, 4 (1) :42-51, 1956.
36. I. S. STRUB and A. M. BAYEN. Weak formulation of boundary conditions for scalar conservation laws. International Journal of Robust and Nonlinear Control, 16:733-748, 2006.
37. P. WILLIAMS, T. WATANABE, C. BLANKSBY, P. TRIVAILO, and H. FUJII. Libration control of flexible tethers using electromagnetic forces and movable attachement. AIAA Journal of Guidance, Control and Dynamics, 27 (5) :882-897, 2004.
38. D. WORK, A. M. BAYEN, AND Q. JACOBSON. Automotive cyber physical systems in the context of human mobility. In National Workshop on high-confidence automotive cyber-physical systems, Troy, MI, April 2008.
39. D. WORK, O. P. TOSSAVAINEN, S. BLANDIN, A. BAYEN, T. IWUCHUKWU, and K. TRACTON. An ensemble Kalman filtering approach to highway traffic estimation using GPS enabled mobile devices. 2008. Submitted to the 47th IEEE Conference on Decision and Control.
40. H. M. ZHANG. A theory of nonequilibrium traffic flow. Transportation Research Part B, 32 (7) :485-498, 1998.