Stability of monotone dynamical flow networks

Proceedings of the IEEE Conference on Decision and Control

Volumn 2015-February, Issue February, 2014, Pages 2384-2389

  Lovisari, Enrico ^a   Como, Giacomo ^b   Savla, Ketan ^c  

^a GIPSA LAB   (France)

^b LUND UNIVERSITY   (Sweden)

^c University of Southern California   (United States)

Author keywords

Dynamical flow network; Monotone systems; Stability; Transportation systems

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; GRAPH THEORY; NUMERICAL ANALYSIS;

CELL TRANSMISSION MODEL; FLOW NETWORK; GLOBALLY ASYMPTOTICALLY STABLE EQUILIBRIUMS; MONOTONE SYSTEMS; STABILITY ANALYSIS; STABILITY PROPERTIES; THROUGHPUT OPTIMALITY; TRANSPORTATION SYSTEM;

STABILITY;

EID: 84926049372     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2014.7039752     Document Type: Conference Paper

References (16)

1. R. Bretherton, K. Wood, and G. Bowen, "Scoot version 4," in Proceedings of 9th International Conference on Road Transport Information and Control, 1998.
2. P. Varaiya, "The max-pressure controller for arbitrary networks of signalized intersections," in Advances in Dynamic Network Modeling in Complex Transportation Systems. Springer, 2013, pp. 27-66.
3. K. Aboudolas, M. Papageorgiou, A. Kouvelas, and E. Kosmatopoulos, "A rolling-horizon quadratic-programming approach to the signal control problem in large-scale congested urban road networks," Transportation Research Part C: Emerging Technologies, Vol. 18, no. 5, pp. 680-694, 2010.
4. S. P. Hoogendoorn and P. H. L. Bovy, "State-of-the-art of vehicular traffic flow modelling," Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, no. 215, pp. 283-303, 2001.
5. D. Helbing, "Traffic and related self-driven many-particle systems," Reviews of Modern Physics, Vol. 73, pp. 1067-1141, 2001.
6. C. F. Daganzo, "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory," Transportation Research B, Vol. 28B, no. 4, pp. 269-287, 1994.
7. -, "The cell transmission model, part II: network traffic," Transportation Research B, Vol. 29B, no. 2, pp. 79-93, 1995.
8. S. Coogan and M. Arcak, "Dynamical properties of a compartmental model for traffic networks," in Proceedings of the American Control Conference, ACC'14, 2014, pp. 2511-2516.
9. M. Hirsch and H. Smith, "Competitive and cooperative systems: A mini-review," Positive Systems. Lecture Notes in Control and Information Sciences, Vol. 294, 2003.
10. G. Gomes, R. Horowitz, A. Kurzhanskiy, P. Varaiya, and J. Kwon, "Behavior of the cell transmission model and effectiveness of ramp metering," Transportation Research Part C, no. 16, pp. 485-513, 2008.
11. D. Pisarski and C. Canudas de Wit, "Analysis and design of equilibrium points for the cell-transmission traffic model," in Proceedings of the American Control Conference, June 2012, pp. 5763-5768.
12. G. Como, E. Lovisari, and K. Savla, "Throughput optimal distributed routing in dynamical flow networks," in Proceedings of the 52th IEEE Conference on Decision and Control, CDC'13, Florence, Italy, 2013, pp. 6729-6734.
13. -, "Throughput optimality and overload behavior of dynamical flow networks under monotone distributed routingg," 2014, accepted at IEEE Transactions on Control of Network Systems.
14. E. Kamke, "Zur theorie der systeme gewoknlicher differentialgliechungen, ii," Acta Mathematica, Vol. 58, pp. 57-85, 1932.
15. H. Khalil, Nonlinear Systems, 3rd ed. Prentice Hall, 2002.
16. R. Beard and V. Stepanyan, "Information consensus in distributed multiple vehicle coordinated control," in Proceedings if the 42nd IEEE Conference on Decision and Control, Vol. 2, December 2003, pp. 2029-2034.