Collaborative Ramp Metering Control: Application to Grenoble South Ring

The thesis presents the results of research on distributed and coordinated control method for freeway ramp metering. The freeway traffic is represented by the Cell-Transmission Model. The primary control objective is to provide a uniform distribution of vehicle densities over freeway links. Density balancing is a new traffic objective which can potentially reduce the number and intensity of acceleration and deceleration events and therefore, it can make a travel more safety and comfortable while decreasing fuel consumption and emissions. In addition, the objective takes into account standard traffic metrics like Total Travel Distance and Total Travel Spent. For the controller, a distributed modular architecture is assumed. It enables to compute the optimal decisions by using only local state information and some supplementary information arriving from the neighbouring controllers.The contributing part begins with the analysis on equilibrium sets of the Cell-Transmission Model. The goal of this study is to derive the conditions that assure the existence and the uniqueness of the balanced equilibrium states. The next step is to find a set of inputs such that the resulting equilibrium state is balanced. In the set of balanced equilibria, we are interested in the selection of the point that maximizes the Total Travel Distance. In the sequel, the implementation aspects and limitations of the proposed method are discussed. Finally, several case studies are presented to support the analysis results and to examine the effectiveness of the proposed method.The major part of the thesis aims on a design of an optimal controller for balancing the traffic density. The optimization is performed in a distributed manner. By using controllability properties, the set of subsystems to be controlled by local ramp meters are identified. The optimization problem is then formulated as a non-cooperative Nash game. The game is solved by decomposing it into a set of two-players hierarchical and competitive games. The process of optimization employs the communication channels matching the switching structure of system interconnectivity. The alternative approach of balancing employs the theory of multi-agent systems. Each of the controllers is provided with a feedback structure assuring that the states within its local subsystem achieve common values by evaluating consensus protocols. Under these structures, an optimal control problem to minimize the Total Travel Spent is formulated. The distributed controller based on the Nash game is validated via Aimsun micro-simulations. The testing scenario involves the traffic data collected from the south ring of Grenoble.

[1]  Nahum Shimkin,et al.  Nonlinear Control Systems , 2008 .

[2]  C. Daganzo THE CELL TRANSMISSION MODEL.. , 1994 .

[3]  Dr. S. M. Aqil Burney Simulation of Systems , 2022 .

[4]  James H Banks EFFECT OF RESPONSE LIMITATIONS ON TRAFFIC-RESPONSIVE RAMP METERING , 1993 .

[5]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[6]  Chai Wah Wu,et al.  Conditions for weak ergodicity of inhomogeneous Markov chains , 2008 .

[7]  Markos Papageorgiou,et al.  Freeway ramp metering: an overview , 2002, IEEE Trans. Intell. Transp. Syst..

[8]  Aaron Strauss Introduction to Optimal Control Theory , 1968 .

[9]  Michael Zhang,et al.  Evaluation of On-ramp Control Algorithms , 2001 .

[10]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[11]  M. L. Chambers The Mathematical Theory of Optimal Processes , 1965 .

[12]  Arnold Neumaier,et al.  Introduction to Numerical Analysis , 2001 .

[13]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[14]  S. Schwartz,et al.  Integrated control of freeway entrance ramps by threshold regulation , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[15]  W. Marsden I and J , 2012 .

[16]  Lianyu Chu,et al.  Optimization of the ALINEA Ramp-metering Control Using Genetic Algorithm with Micro-simulation , 2003 .

[17]  Antonella Ferrara,et al.  Freeway networks as Systems of Systems: An event-triggered distributed control scheme , 2012, 2012 7th International Conference on System of Systems Engineering (SoSE).

[18]  Anders Rantzer,et al.  Distributed control of positive systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[19]  Carlos Canudas-de-Wit,et al.  Optimal balancing of road traffic density distributions for the Cell Transmission Model , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[20]  Carlos Canudas de Wit,et al.  Optimal Control of Systems of Conservation Laws and Application to Non-Equilibrium Traffic Control , 2006 .

[21]  J. Meditch,et al.  Applied optimal control , 1972, IEEE Transactions on Automatic Control.

[22]  S. Kahne,et al.  Optimal control: An introduction to the theory and ITs applications , 1967, IEEE Transactions on Automatic Control.

[23]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[24]  Bart De Schutter,et al.  Non-Linear Model Predictive Control Based on Game Theory for Traffic Control on Highways , 2012 .

[25]  Christian G. Claudel,et al.  Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks , 2014, IEEE Transactions on Control of Network Systems.

[26]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[27]  S. Liberty,et al.  Linear Systems , 2010, Scientific Parallel Computing.

[28]  P. Berck,et al.  Calculus of variations and optimal control theory , 1993 .

[29]  Louis E Lipp,et al.  BENEFITS OF CENTRAL COMPUTER CONTROL FOR DENVER RAMP-METERING SYSTEM , 1991 .

[30]  C. C. Wit,et al.  OPTIMAL RAMP METERING STRATEGY WITH EXTENDED LWR MODEL, ANALYSIS AND COMPUTATIONAL METHODS , 2005 .

[31]  H. Greenberg An Analysis of Traffic Flow , 1959 .

[32]  Markos Papageorgiou,et al.  Hero coordinated ramp metering implemented at the Monash Freeway , 2010 .

[33]  Roberto Horowitz,et al.  Behavior of the cell transmission model and effectiveness of ramp metering , 2008 .

[34]  William H. Press,et al.  Book-Review - Numerical Recipes in Pascal - the Art of Scientific Computing , 1989 .

[35]  L. Giovanini Game approach to distributed model predictive control , 2011 .

[36]  Adolf D May,et al.  COMPUTER MODEL FOR OPTIMAL FREEWAY ON-RAMP CONTROL , 1973 .

[37]  S. K. Zegeye,et al.  09-049 Model-based traffic control for the reduction of fuel consumption , emissions , and travel time ∗ , 2009 .

[38]  Markos Papageorgiou,et al.  ALINEA Local Ramp Metering: Summary of Field Results , 1997 .

[39]  P J Wong,et al.  GUIDELINES FOR DESIGN AND OPERATION OF RAMP CONTROL SYSTEMS , 1975 .

[40]  R. Sundaram A First Course in Optimization Theory: Bibliography , 1996 .

[41]  Roberto Horowitz,et al.  Optimal freeway ramp metering using the asymmetric cell transmission model , 2006 .

[42]  B. Piccoli Necessary conditions for hybrid optimization , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[43]  Roberto Horowitz,et al.  Optimal control of freeway networks based on the Link Node Cell transmission model , 2012, 2012 American Control Conference (ACC).

[44]  Victor M. Becerra,et al.  Optimal control , 2008, Scholarpedia.

[45]  C. Wang On a Ramp-Flow Assignment Problem , 1972 .

[46]  E. T. WHITTAKER,et al.  Partial Differential Equations of Mathematical Physics , 1932, Nature.

[47]  M. Hestenes Calculus of variations and optimal control theory , 1966 .

[48]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[49]  V. Borkar,et al.  A unified framework for hybrid control: model and optimal control theory , 1998, IEEE Trans. Autom. Control..

[50]  Zhongren Wang,et al.  Ramp Metering Status in California , 2013 .

[51]  Arnold RAMP METERING: A REVIEW OF THE LITERATURE , 1998 .

[52]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[53]  Tao Jiang,et al.  Fuzzy Self-Adaptive PID Controller for Freeway Ramp Metering , 2009, 2009 International Conference on Measuring Technology and Mechatronics Automation.

[54]  H. Sussmann,et al.  A maximum principle for hybrid optimal control problems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[55]  P. Olver Nonlinear Systems , 2013 .

[56]  Liping Fu,et al.  An Efficient Optimization Approach to Real-Time Coordinated and Integrated Freeway Traffic Control , 2010, IEEE Transactions on Intelligent Transportation Systems.

[57]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[58]  Zheng Li,et al.  Freeway Ramp Control Based on Genetic PI and Fuzzy Logic , 2008, 2008 IEEE Pacific-Asia Workshop on Computational Intelligence and Industrial Application.

[59]  M. Branicky,et al.  Algorithms for optimal hybrid control , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[60]  J. Lions Optimal Control of Systems Governed by Partial Differential Equations , 1971 .

[61]  Sean R Eddy,et al.  What is dynamic programming? , 2004, Nature Biotechnology.

[62]  Martin Treiber,et al.  Traffic Flow Dynamics , 2013 .

[63]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[64]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[65]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[66]  Eduardo F. Camacho,et al.  Global Versus Local MPC Algorithms in Freeway Traffic Control With Ramp Metering and Variable Speed Limits , 2012, IEEE Transactions on Intelligent Transportation Systems.

[67]  B D Greenshields,et al.  A study of traffic capacity , 1935 .

[68]  Alexandre M. Bayen,et al.  A dual decomposition method for sector capacity constrained traffic flow optimization , 2011 .

[69]  Hector O. Fattorini,et al.  Infinite Dimensional Optimization and Control Theory: References , 1999 .

[70]  M. Krstić,et al.  Optimal control of scalar one-dimensional conservation laws , 2006, 2006 American Control Conference.

[71]  Deirdre R. Meldrum,et al.  FREEWAY TRAFFIC DATA PREDICTION USING ARTIFICIAL NEURAL NETWORKS AND DEVELOPMENT OF A FUZZY LOGIC RAMP METERING ALGORITHM , 1995 .

[72]  Semyon M. Meerkov,et al.  Feedback control of highway congestion by a fair on-ramp metering , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[73]  Stephen P. Boyd,et al.  Fast Model Predictive Control Using Online Optimization , 2010, IEEE Transactions on Control Systems Technology.

[74]  Kai Zhang,et al.  Optimizing Traffic Control to Reduce Fuel Consumption and Vehicular Emissions , 2009 .

[75]  J. Lebacque THE GODUNOV SCHEME AND WHAT IT MEANS FOR FIRST ORDER TRAFFIC FLOW MODELS , 1996 .

[76]  Changsong Deng,et al.  Statistics and Probability Letters , 2011 .

[77]  Markos Papageorgiou,et al.  ALINEA: A LOCAL FEEDBACK CONTROL LAW FOR ON-RAMP METERING , 1990 .

[78]  Edmund Taylor Whittaker,et al.  On the partial differential equations of mathematical physics , 1903 .

[79]  A. Hegyi,et al.  Optimal coordination of ramp metering and variable speed control-an MPC approach , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[80]  Harold J Payne,et al.  MODELS OF FREEWAY TRAFFIC AND CONTROL. , 1971 .

[81]  R. LeVeque Numerical methods for conservation laws , 1990 .

[82]  Anders Rantzer,et al.  Dynamic dual decomposition for distributed control , 2009, 2009 American Control Conference.

[83]  M. Cremer,et al.  A State Feedback Approach to Freeway Traffic Control , 1978 .

[84]  H. M. Zhang,et al.  Some general results on the optimal ramp control problem , 1996 .

[85]  Anders Rantzer,et al.  Piecewise linear quadratic optimal control , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[86]  Ludovic Leclercq,et al.  Capacity drops at merges: An endogenous model , 2011 .

[87]  Gang Feng,et al.  Consensus of Multi-Agent Networks With Aperiodic Sampled Communication Via Impulsive Algorithms Using Position-Only Measurements , 2012, IEEE Transactions on Automatic Control.