Asymptotic stability of constant time headway driving strategy with multiple driver reaction delays

Proceedings of the American Control Conference

Volumn , Issue , 2009, Pages 4898-4903

  Sipahi, Rifat ^a   Niculescu, Silviu Iulian ^b   Delice, Ismail Ilker ^a  

^a Northeastern University   (United States)

^b UNIV PARIS SUD   (France)

Author keywords

Car following; Delay; Stability; Traffic dynamics

Indexed keywords

CAR FOLLOWING; CAR-FOLLOWING MODELS; CONSTANT TIME; CONTINUOUS TIME; DELAY PARAMETERS; DRIVER REACTION; DRIVING BEHAVIOR; DRIVING STRATEGY; ILLUSTRATIVE EXAMPLES; STABILITY ANALYSIS; STABILITY REGIONS; TRAFFIC DYNAMICS;

ASYMPTOTIC ANALYSIS; ASYMPTOTIC STABILITY; TRAFFIC CONTROL;

AUTOMOBILE DRIVERS;

EID: 70449719581     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACC.2009.5160482     Document Type: Conference Paper

References (41)

1. M. Bando, K. Hasebe, K. Nakanishi, A. Nakayama, "Analysis of Optimal Velocity Model with Explicit Delay," Phy Rev E, 58, 5429-5435, 1998.
2. R. E. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York, 1963.
3. A. Bose, and P.A. Ioannou, "Analysis of Traffic Flow With Mixed Manual and Semiautomated Vehicles", IEEE Int. Trans. Sys., 4(4), 173-188, 2003.
4. R.E. Chandler, R. Herman, E.W. Montroll, "Traffic Dynamics: Studies in Car Following," Oper. Res., 7(1), 165-184, 1958.
5. J. Chen, H.A. Latchman, "Frequency sweeping tests for stability independent of delay," IEEE Trans. Automat. Contr., 40, 1640-1645, 1995.
6. P.A. Cook, "Stable Control of Vehicle Convoys for Safety and Comfort", IEEE Trans. Automat. Contr., 52(3), 526-531, 2007.
7. L.C. Davis, "Modifications of the Optimal Velocity Traffic Model to Include Delay Due to Driver Reaction Time," Physica A, 319, 557-567, 2003.
8. H. Fazelinia and R. Sipahi and N. Olgac, "Stability analysis of multiple time-delayed systems using 'Building Block' concept", IEEE Trans. Automat. Contr., 52(5), 799-810, 2007.
9. M. Green, "How Long Does It Take to Stop?" Methodological Analysis of Driver Perception-Brake Times," Trans. Human Fact., 2, 195-216, 2000.
10. K. Gu, V.L. Kharitonov, J. Chen, Stability of Time-Delay Systems. Birkhauser: Boston, 2003.
11. K. Gu and S.-I. Niculescu, "Survey on recent results in the stability and control of time-delay systems", J. Dyn. Sys., Meas. Cont., 125(2), 158-165, 2003.
12. K. Gu and S.-I. Niculescu and J. Chen, "On stability crossing curves for general systems with two delays", J. Math. Anal. Appl., 311(1), 231-253, 2005.
13. J. K. Hale and S. M. Verduyn Lunel, An Introduction to Functional Differential Equations, Applied Mathematical Sciences, vol. 99, Springer-Verlag, New York, 1993.
14. D. Helbing, Traffic and Related Self-Driven Many-Particle Systems, Rev. Mod. Phy., 73, 1067-1141, 2001.
15. K. Konishi, H. Kokame, K. Hirata, "Decentralized Delayed-Feedback Control of an Optimal Velocity Traffic Model," Euro. Phys. J. B, 15, 715-722, 2000.
16. W. Michiels, S.-I. Niculescu, Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach, SIAM Advances in Design and Control vol. 12, Philadelphia, 2007.
17. S.-I. Niculescu, Delay Effects on Stability: A Robust Control Approach. Springer-Verlag: Heidelberg, LNCIS, 269, 2001.
18. N. Olgac, R. Sipahi, "An exact method for the stability analysis of time delayed LTI systems", IEEE Trans. Automat. Contr., 47(5), 793-797, 2002.
19. N. Olgac, R. Sipahi, "An improved procedure in detecting the stability robustness of systems with uncertain delay", IEEE Trans. Automat. Contr., 51(7), 1164-1165, 2006.
20. G. Orosz, G. Stepan, "Hopf bifurcation calculations in delayed systems with translational symmetry", J. Nonlin. Sci., 14(6), 505-528, 2004.
21. G. Orosz, R.E. Wilson, B., Krauskopf, "Global Bifurcation Investigation of an Optimal Velocity Traffic Model with Driver Reaction Time," Phys. Rev. E, 70(2), Art. No. 026207 Part 2, 2004.
22. L.A. Pipes, "An operational analysis of traffic dynamics," J. Appl. Phys., 24, pp. 274-281, 1953.
23. R.W. Rothery, "Transportation Research Board (Trb) Special Report 165," in Traffic Flow Theory, 2nd Edition, N. H. Gartner, C. J. Messner, and A. J. Rathi, Eds., 1998.
24. K. Santhanakrishnan, and R. Rajamani, "On Spacing Policies for Highway Vehicle Automation", IEEE Int. Trans. Sys., 4(4), 198-204, 2003.
25. P. Seiler, A. Pant, K. Hedrick, "Disturbance Propagation in Vehicle Strings", IEEE Trans. Automat. Contr., 49(10), 1835-1842, 2004.
26. R. Sipahi, S.-I. Niculescu, "Slow Time-Varying Delay Effects - Robust Stability Characterization of Deterministic Car Following Models", IEEE Int. Conf. Cont. Appl., 2006, Munich, Germany.
27. R. Sipahi, S.-I. Niculescu, "Analytical Stability Study of a Deterministic Car Following Model under Multiple Delay Interactions," at Invited Session Traffic Dynamics under Presence of Time Delays, IFAC Time Delay Systems Workshop, 2006, Italy.
28. R. Sipahi, F.M. Atay, S.-I. Niculescu, "Stability of Traffic Flow with Distributed Delays Modeling the Memory Effects of the Drivers," SIAM Appl. Math., 68(3), 738-759, 2007.
29. R. Sipahi, N. Olgac, "Kernel and offspring concepts for the stability robustness of multiple time delayed systems (MTDS)", J. Dyn. Sys., Meas. Cont., 129(3), 245-251, 2007.
30. R. Sipahi, N. Olgac, "Complete stability robustness of third-order LTI multiple time-delay systems", Automatica, 41(8), 1413-1422, 2005.
31. R. Sipahi, S.-I. Niculescu, "Chain Stability in Traffic Flow with Driver Reaction Delays", American Control Conference, Seattle, WA, 2008.
32. R. Sipahi, I.I. Delice, "Extraction of 3D stability switching hypersurfaces of a time delay system with multiple fixed delays", Automatica, available online.
33. R. Sipahi, I.I. Delice and S.-I. Niculescu, "Asymptotic Stability of Constant Time Headway Driving Strategy with Multiple Driver Reaction Delays", submitted to IEEE Int. Trans. Sys..
34. S.S. Stankovic, M.J. Stanojevic, D.D. Siljak, "Decentralized Overlapping Control of a Platton of Vehicles", IEEE Cont. Sys. Tech., 8(5), 2000.
35. R. Subramanian, "Motor Vehicle Traffic Crashes as a Leading Cause of Death in the United States, 2002", Traffic Safety Facts, Research note, National Highway Traffic Safety Administration (NHTSA), 2005.
36. D. Swaroop, J.K. Hedrick, S.B. Choi, "Direct Adaptive Longitudinal Control of Vehicle Platoons", IEEE Vehic. Tech., 50(1), 2001.
37. D. Swaroop, J. K. Hedrick, "String Stability of Interconnected Systems", IEEE Trans. Automat. Contr., 41(3), 1996.
38. M. Treiber, D. Helbing, "Memory Effects in Microscopic Traffic Models and Wide Scattering in Flow-Density Data," Phys. Rev. E, 68, 46119/1-46119/8, 2003.
39. M. Treiber, A. Kesting, D. Helbing, "Delays, Inaccuracies and Anticipation in Microscopic Traffic Models", Physica A, 360(1), 71-88, doi:10.1016/j.physa.2005.05.001, 2006.
40. D. Yankiev, I. Kanellakopoulos, "Nonlinear Spacing Policies for Automated Heavy-Duty Vehicles", IEEE Vehic. Tech., 47(4), 1998.
41. J. Zhou, H. Peng, "Range Policy of Adaptive Cruise Control Vehicles for Improved Flow Stability and String Stability", IEEE Intel. Trans. Sys., 6(2), 2005.