A Continuous Petri Net Approach for Model Predictive Control of Traffic Systems

Traffic systems are often highly populated discrete event systems that exhibit several modes of behavior such as free flow traffic, traffic jams, stop-and-go waves, etc. An appropriate closed loop control of the congested system is crucial in order to avoid undesirable behavior. This paper proposes a macroscopic model based on continuous Petri nets as a tool for designing control laws that improve the behavior of traffic systems. The main reason to use a continuous model is to avoid the state explosion problem inherent to large discrete event systems. The obtained model captures the different operation modes of a traffic system and is highly compositional. In order to handle the variability of the traffic conditions, a model predictive control strategy is proposed and validated.

[1]  Mariagrazia Dotoli,et al.  An urban traffic network model by first order hybrid Petri nets , 2008, 2008 IEEE International Conference on Systems, Man and Cybernetics.

[2]  Serge P. Hoogendoorn,et al.  State-of-the-art of vehicular traffic flow modelling , 2001 .

[3]  Manuel Silva,et al.  Introducing Petri nets , 1993 .

[4]  Markos Papageorgiou,et al.  Traffic flow modeling of large-scale motorwaynetworks using the macroscopic modeling tool METANET , 2002, IEEE Trans. Intell. Transp. Syst..

[5]  Markos Papageorgiou,et al.  Applications of Automatic Control Concepts to Traffic Flow Modeling and Control , 1983 .

[6]  Mariagrazia Dotoli,et al.  An urban traffic network model via coloured timed Petri nets , 2004 .

[7]  Jan M. Maciejowski,et al.  Predictive control : with constraints , 2002 .

[8]  Manuel Silva Suárez,et al.  On fluidification of Petri Nets: from discrete to hybrid and continuous models , 2003, Annu. Rev. Control..

[9]  Hongye Su,et al.  Supervisor Synthesis for Enforcing a Class of Generalized Mutual Exclusion Constraints on Petri Nets , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[10]  Hassane Alla,et al.  Discrete, continuous, and hybrid Petri Nets , 2004 .

[11]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[12]  Angela Di Febbraro,et al.  Urban traffic control structure based on hybrid Petri nets , 2004, IEEE Transactions on Intelligent Transportation Systems.

[13]  Alessandro Giua,et al.  First-order hybrid Petri nets: a model for optimization and control , 2000, IEEE Trans. Robotics Autom..

[14]  Anthony Tzes,et al.  Applications of Petri networks to transportation network modeling , 1996 .

[15]  C. Daganzo.  A finite difference approximation of the kinematic wave model of traffic flow , 1995 .

[16]  S. Joe Qin,et al.  A survey of industrial model predictive control technology , 2003 .

[17]  T. Kato,et al.  Large-Scale Traffic Network Control Based on Mixed Integer Non-linear System Formulation , 2006, IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics.

[18]  Dirk Helbing.  TRAFFIC DATA AND THEIR IMPLICATIONS FOR CONSISTENT TRAFFIC FLOW MODELING , 1997 .

[19]  Simon Peck,et al.  Practice of Petri Nets in Manufacturing , 1993 .

[20]  Jean-Loup Farges,et al.  Design by Petri nets of an intersection signal controller , 1996 .

[21]  René Boel,et al.  MODELLING AND CONTROLLING TRAFFIC BEHAVIOUR WITH CONTINUOUS PETRI NETS , 2005 .

[22]  Dimitri Lefebvre,et al.  Continuous and timed Petri nets for the macroscopic and microscopic traffic flow modelling , 2005, Simul. Model. Pract. Theory.

[23]  Shigeru Okuma,et al.  Traffic Network Control Based on Hybrid Dynamical System Modeling and Mixed Integer Nonlinear Programming With Convexity Analysis , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[24]  John W. Fowler,et al.  Petri Net Translation Patterns for the Analysis of eBusiness Collaboration Messaging Protocols , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[25]  Manuel Silva,et al.  On Fluidification of Petri Nets: From Discrete to Hybrid and Continuous Models , 2003, ADHS.