Robust Control for Urban Road Traffic Networks

The aim of the presented research is to elaborate a traffic-responsive optimal signal split algorithm taking uncertainty into account. The traffic control objective is to minimize the weighted link queue lengths within an urban network area. The control problem is formulated in a centralized rolling-horizon fashion in which unknown but bounded demand and queue uncertainty influences the prediction. An efficient constrained minimax optimization is suggested to obtain the green time combination, which minimizes the objective function when worst case uncertainty appears. As an illustrative example, a simulation study is carried out to demonstrate the effectiveness and computational feasibility of the robust predictive approach. By using real-world traffic data and microscopic traffic simulator, the proposed robust signal split algorithm is analyzed and compared with well-tuned fixed-time signal timing and to nominal predictive solutions under different traffic conditions.

[1]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[2]  Markos Papageorgiou,et al.  A rolling-horizon quadratic-programming approach to the signal control problem in large-scale congested urban road networks , 2008 .

[3]  E. Aiyoshi,et al.  Necessary conditions for min-max problems and algorithms by a relaxation procedure , 1980 .

[4]  J. Lofberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).

[5]  Yafeng Yin,et al.  Robust optimal traffic signal timing , 2008 .

[6]  Yafeng Yin,et al.  Robust Signal Timing for Arterials under Day-to-Day Demand Variations , 2010 .

[7]  Maxwell G. Lay,et al.  Handbook of road technology , 1986 .

[8]  D. Gazis.  Optimum Control of a System of Oversaturated Intersections , 1964 .

[9]  R B Potts,et al.  THE OVERSATURATED INTERSECTION , 1963 .

[10]  Markos Papageorgiou,et al.  Real-time estimation of vehicle-count within signalized links , 2008 .

[11]  Tamás Péni,et al.  MPC in Urban Traffic Management , 2010 .

[12]  Bart De Schutter,et al.  Fast Model Predictive Control for Urban Road Networks via MILP , 2011, IEEE Transactions on Intelligent Transportation Systems.

[13]  Eduardo F. Camacho,et al.  Min-Max MPC using a tractable QP Problem , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[14]  Jing-Quan Li.  Discretization modeling, integer programming formulations and dynamic programming algorithms for robust traffic signal timing , 2011 .

[15]  J. Löfberg.  Minimax approaches to robust model predictive control , 2003 .

[16]  Bart De Schutter,et al.  Efficient network-wide model-based predictive control for urban traffic networks , 2012 .

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

[18]  István Varga,et al.  ESTIMATION OF DYNAMIC ORIGIN DESTINATION MATRIX OF TRAFFIC SYSTEMS , 2005 .

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

[20]  Markos Papageorgiou,et al.  Coordinated ramp metering for freeway networks – A model-predictive hierarchical control approach , 2010 .

[21]  Carlos F. Daganzo,et al.  THE CELL TRANSMISSION MODEL, PART II: NETWORK TRAFFIC , 1995 .

[22]  J. Bokor,et al.  CONSTRAINED SPLIT RATE ESTIMATION BY MOVING HORIZON , 2005 .

[23]  Markos Papageorgiou,et al.  Store-and-forward based methods for the signal control problem in large-scale congested urban road networks , 2009 .

[24]  S. Vavasis.  Nonlinear optimization: complexity issues , 1991 .

[25]  A Convex Relaxation of a Minimax MPC Controller , 2001 .

[26]  Lucas Barcelos de Oliveira,et al.  Multi-agent Model Predictive Control of Signaling Split in Urban Traffic Networks ∗ , 2010 .

[27]  Benjamin Heydecker,et al.  Uncertainty and variability in traffic signal calculations , 1987 .

[28]  Laurent El Ghaoui,et al.  Robust Solutions to Uncertain Semidefinite Programs , 1998, SIAM J. Optim..

[29]  Johan Efberg,et al.  YALMIP : A toolbox for modeling and optimization in MATLAB , 2004 .

[30]  Satish V. Ukkusuri,et al.  A robust transportation signal control problem accounting for traffic dynamics , 2010, Comput. Oper. Res..

[31]  Wang,et al.  Review of road traffic control strategies , 2003, Proceedings of the IEEE.

[32]  Makoto Yamashita,et al.  A high-performance software package for semidefinite programs: SDPA 7 , 2010 .

[33]  Nikolas Geroliminis,et al.  Optimal Perimeter Control for Two Urban Regions With Macroscopic Fundamental Diagrams: A Model Predictive Approach , 2013, IEEE Transactions on Intelligent Transportation Systems.

[34]  P. C. M. Ribeiro.  HANDLING TRAFFIC FLUCTUATION WITH FIXED-TIME PLANS CALCULATED BY TRANSYT , 1994 .

[35]  J. Bokor,et al.  Model predictive control in urban traffic network management , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[36]  Markos Papageorgiou,et al.  Cost Effective Real-Time Traffic Signal Control Using the TUC Strategy , 2010, IEEE Intelligent Transportation Systems Magazine.