Abstract
Road traffic networks are large-scale systems that demand distributed control strategies. Distributed model predictive control (DMPC) arises as a feasible alternative for traffic control. Distributed strategies decompose the whole traffic network into different subnetworks with local optimal controllers that make decisions on actions to be taken by the actuators responsible for traffic control (traffic lights, routing signals, variable speed limits, among others). However, subnetworks are interacting elements of the whole traffic network. Hence, local control decisions made for one sub-network affect and are influenced by the decisions taken for the other subnetworks. Under these circumstances, the DMPC traffic problem can be treated as a game where the rules are provided by the physical system, the players are the local optimal controllers, their strategies are the control sequences, and the payoffs are the local performance indices (such as the total time spent by the users in the network). This configuration allows the achievement of a computational burden reduction, with a compromise between local and global performance. Since DMPC local controllers are able to communicate with each other, the control of the traffic network corresponds to a cooperative game. In this chapter, game-theory-based DMPC is developed and tested for control of urban and motorway networks.
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References
Akira O (2005) A noncooperative approach to general n-person cooperative games. Discussion papers 2005-01, Graduate School of Economics, Hitotsubashi University
Baskar LD, De Schutter B, Hellendoorn J (2009) Optimal routing for intelligent vehicle highway systems using a macroscopic traffic flow model. In: 12th international IEEE conference on intelligent transportation systems, ITSC ‘09, pp 1–6. doi:10.1109/ITSC.2009.5309657
Bellemans T, De Schutter B, De Moor B (2006) Model predictive control for ramp metering of motorway traffic: a case study. Control Eng Pract 140(7):757–767. doi:10.1016/j.conengprac.2005.03.010
Camponogara E, Jia D, Krogh BH, Talukdar S (2002) Distributed model predictive control. IEEE Control Syst Mag 22(1):44–52
Du X, Xi Y, Li S (2001) Distributed model predictive control for large-scale systems. In: Proceedings of the 2001 American control conference, Arlington, USA, 25–27 June, pp 3142–3143
Ferrara A, Nai Oleari A, Sacone S, Siri S (2012) Freeway networks as systems of systems: an event-triggered distributed control scheme. In: Proceedings of the 7th IEEE conference on system of systems engineering, Genoa, Italy, July 2012, pp 197–202
Frejo JRD, Camacho EF (2012) Global versus local MPC algorithms in freeway traffic control with ramp metering and variable speed limits. IEEE Trans Intell Transp Syst 130(4):1556–1565
Giovanini L, Balderud J (2006) Game approach to distributed model predictive control. In: Proceedings of the international control conference, Glasgow, Scotland, 30th Aug–1st Sept 2006
Groot N, De Schutter B, Zegeye SK, Hellendoorn H (2011) Model-based traffic and emission control using pwa models: a mixed-logical dynamic approach. In: 14th international IEEE conference on intelligent transportation systems (ITSC), Oct 2011, pp 2142–2147. doi:10.1109/ITSC.2011.6082809
Haj-Salem H, Poirier P, Heylliard J-F, Peynaud J-P (2001) Alinea: a local traffic responsive strategy for ramp metering. field results on a6 motorway in paris. In: Proceedings 2001 IEEE intelligent transportation systems, pp 106–111. doi:10.1109/ITSC.2001.948638
Harsanyi JC (1963) A simplified bargaining model for the n-person cooperative game. Int Econ Rev 40(2):194–220
Hegyi A, De Schutter B, Hellendoorn H, Van den Boom T (2002) Optimal coordination of ramp metering and variable speed control-an mpc approach. In: Proceedings of the 2002 American control conference, vol 5, pp 3600–3605. doi: 10.1109/ACC.2002.1024487
Hegyi A, De Schutter B, Hellendoorn H (2005) Model predictive control for optimal coordination of ramp metering and variable speed limits. Transp Res Part C 130(3):185–209. doi:10.1016/j.trc.2004.08.001
Jia D, Krogh BH (2001) Distributed model predictive control. In: Proceedings of the 2001 American control conference, Arlington, USA, 25–27 June, pp 2767–2772
Long K, Yun M, Zheng J, Yang X (2008) Model predictive control for variable speed limit in freeway work zone. In: 27th Chinese control conference, CCC 2008, July 2008, pp 488–493. doi:10.1109/CHICC.2008.4605219
Kotsialos A, Papageorgiou M, Messmer A (1999) Optimal coordinated and integrated motorway network traffic control. In: Proceedings of the 14th international symposium on transportation and traffic theory (ISTTT), Jerusalem, Israel, pp 621–644
Kotsialos A, Papageorgiou M, Diakaki C, Pavlis Y, Middelham F (2002) Traffic flow modeling of large-scale motorway networks using the macroscopic modeling tool metanet. IEEE Trans Intell Transp Syst 30(4):282–292
Kotsialos A, Papageorgiou M, Mangeas M, Haj-Salem H (2002) Coordinated and integrated control of motorway networks via non-linear optimal control. Transp Res Part C 10:65–84
Li S, Zhang Y, Zhu Q (2005) Nash-optimization enhanced distributed model predictive control applied to the Shell benchmark problem. Inf Sci 1700(2–4):329–349
Lin S (2011) Efficient model predictive control for large-scale urban traffic networks. PhD thesis, Delft University of Technology, Delft
Lin S, De Schutter B, Xi Y, Hellendoorn H (2011) Fast model predictive control for urban road networks via MILP. IEEE Trans Intell Transp Syst 120(3):846–856. doi:10.1109/TITS.2011.2114652 ISSN 1524-9050
Lin S, De Schutter B, Xi Y, Hellendoorn H (2012) Efficient network-wide model-based predictive control for urban traffic networks. Transp Res Part C: Eemerg Technol 240:122–140. ISSN 0968-090X. doi:http://dx.doi.org/10.1016/j.trc.2012.02.003. URL http://www.sciencedirect.com/science/article/pii/S0968090X12000150
Lu X-Y, Qiu TZ, Varaiya P, Horowitz R, Shladover SE (2010) Combining variable speed limits with ramp metering for freeway traffic control. In: American control conference (ACC), June 2010, pp 2266–2271
Maestre JM, Muñoz de la Peña D, Camacho EF (2011) Distributed model predictive control based on a cooperative game. Optimal Control Appl Methods 320(2):153–176
Maestre JM, Muñoz de la Peña D, Jiménez Losada A, Algaba Durán E, Camacho EF (2011) An application of cooperative game theory to distributed control. In: Proceedings of the 18th IFAC world congress, Milan, pp 9121–9126
Maestre JM, Muñoz de la Peña D, Camacho EF, Alamo T (2011) Distributed model predictive control based on agent negotiation. J Process Control 10(5):685–697
Muñoz de la Peña JM, Maestre D, Camacho EF (2009) Distributed MPC based on a cooperative game. In: Proceedings of the 48th IEEE conference on decision and control and 28th Chinese control conference, Shanghai, 15–18 Dec, pp 5390–5395
Myerson RB (1991) Game theory: analysis of conflict. Harvard University Press, Canbridge. ISBN 978-0-674-34116-6
Nash J (1950) The bargaining problem. Econometrica 180(2):155–162
J Nash (1950) Equilibrium points in N-persons games. In: Proc Nat Acad Sci USA 360(1):40–48
Nash J (1953) Two-person cooperative games. Econometrica 210(1):128–140
Necoara I, Doan D, Suykens JAK (2008) Application of the proximal center decomposition method to distributed model predictive control. In: Proceedings of the 2008 IEEE conference on decision and control, Cancun, 9–11 Dec, pp 2900–2905
Negenborn RR, De Schutter B, Hellendoorn J (2008) Multi-agent model predictive control for transportation networks: serial versus parallel schemes. Eng Appl Artif Intell 210(3):353–366
Papageorgiou M, Blosseville JM, Haj-Salemn H (1990) Modelling and real-time control of traffic flow on the southern part of boulevard peripherique in Paris: part ii: coordinated on-ramp metering. Transp Res Part A 240(5):361–370
Papageorgiou M, Kosmatopoulos E, Papamichail I, Wang Y (2008) A misapplication of the local ramp metering strategy alinea. Intell Transp Syst IEEE Trans 90(2):360–365. doi:10.1109/TITS.2008.922975 ISSN 1524-9050
Peters HJM (1992) Axiomatic bargaining game theory. Kluwer Academic Publishers, Dordrecht
Pimentel J, Salazar M (2002) Dependability of distributed control system fault tolerant units. Proc IECON 4:3164–3169
Portilla C, Valencia F, López JD, Espinosa J, Núñez A, De Schutter B (2012) Non-linear model predictive control based on game theory for traffic control on highways. In: Proceedings of the 4th IFAC nonlinear model predictive control conference, pp 436–441
Rantzer A (2006) Linear quadratic team theory revisited. In: Proceedings of the 2006 American control conference, Minneapolis, 14–16 June 2006
Rantzer A (2088) Using game theory for distributed control engineering. In: Proceedings of the 3rd world congress of the game theory society, Evanston, July 2008, pp 13–17
Rantzer A (2009) Dynamic dual decomposition for distributed control. In: Proceedings of the American control conference 2009, St Louis, 10–12 June, pp 884–888
Talukdar S, Jia D, Hines P, Krogh BH (2005) Distributed model predictive control for the mitigation of cascading failures. In: Proceedings of the 44th IEEE conference on decision and control, and the 2005 European control conference, Seville, 12–15 Dec, pp 4440–4445
Treiber M, Kesting A (2013) Traffic flow dynamics. Springer, Berlin
Trodden PA, Nicholson D, Richards AG (2009) Distributed model predictive control as a game with coupled contraints. In: Proceedings of the European control conference, Budapest, 23–26 Aug 2009
Valencia F (2012) Game theory based distributed model predictive control: an approach to large-scale systems control. PhD thesis, Facultad de Minas, Universidad Nacional de Colombia, Medellín
Valencia F, Espinosa JJ, De Schutter B, Staňková K (2011) Feasible-cooperation distributed model predictive control scheme based on game theory. In: Proceedings of the 18th IFAC world congress, Milan, pp 386–391
van den Berg M, Hegyi A, De Schutter B, Hellendoorn J (2003) A macroscopic traffic flow model for integrated control of freeway and urban traffic networks. In: Proceedings of the 42nd IEEE conference on decision and control, Maui, 09–12 Dec 2003, pp 2774–2779
Venkat AN, Rawlings JB, Wright SJ (2006) Implementable distributed model predictive control with guaranteed performance properties. In: Proceedings of the 2006 American control conference, Minneapolis, 14–16 June, pp 613–618
Venkat AN, Hiskens IA, Rawlings JB, Wright SJ (2006) Distributed MPC strategies for automatic generation control. In: Proceedings of the IFAC symposium on power plants and power systems control, Canada, pp 383–388
Venkat AN, Rawlings JB, Wright SJ (2006) Stability and optimality of distributed, linear model predictive control. Part I: state feedback. In: Texas-Wisconsin modeling and control consortium technical report 3
Von Neumann J, Morgenstern O, Kuhn HW, Rubinstein A (1947) Theory of games and economic behavior. Princeton University Press, Princeton
Wang FY, Cameron IT (2007) A multi-form modelling approach to the dynamics and control of drum granulation processes. Powder Technol 1790(1–2):2–11
Yang SH, Chen X, Alty JL (2003) Design issues and implementation of Internet-based process control systems. Control Eng Pract 110(6):709–720
Zegeye SK, De Schutter B, Hellendoorn J, Breunesse EA, Hegyi A (2012) A predictive traffic controller for sustainable mobility using parameterized control policies. IEEE Trans Intell Transp Syst 130(3):1420–1429. doi:10.1109/TITS.2012.2197202
Acknowledgments
Research supported by: COLCIENCIAS project Modelamiento y control de tráfico urbano en la ciudad de Medellín, código 1118-569-34640, CT 941-2012; the European 7th Framework Network of Excellence Highly complex and networked control systems (HYCON2) grant agreement No. 257962, by the European COST Action TU1102, and by the Solar Energy Research Center SERC-CHILE, FONDAP project 15110019.
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Valencia, F. et al. (2015). Congestion Management in Motorways and Urban Networks Through a Bargaining-Game-Based Coordination Mechanism. In: Hausken, K., Zhuang, J. (eds) Game Theoretic Analysis of Congestion, Safety and Security. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-11674-7_1
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