Perimeter Control of Multiregion Urban Traffic Networks With Time-Varying Delays

In this paper, an adaptive perimeter control problem is studied for urban traffic networks with multiple regions, time-varying state, and input delays. After defining state variables by partition the accumulation variable of each region, a system model is formulated as nonlinear ordinary differential equations based on the concept of macroscopic fundamental diagram. Both the travel times of vehicles as well as evacuation process of traffic jams are first introduced into the system dynamics, and they are modeled as input and state delays, respectively. The control objective is to stabilize the number of vehicles in each region to desired values. By employing the model reference adaptive control scheme and asymptotical sliding mode technique, two filters and adaptive laws for control parameters are designed by using only the information of the reference model. With properly constructed Lyapunov functions, the stability of tracking error with regard to the reference signals is analyzed. Lastly, a simulation example is given to demonstrate the effectiveness of the proposed methods.

[1]  Jinde Cao,et al.  LMI-based criteria for global robust stability of bidirectional associative memory networks with time delay , 2007 .

[2]  Nikolaos Geroliminis,et al.  Properties of a well-defined Macroscopic Fundamental Diagram for urban traffic , 2011 .

[3]  Shengyuan Xu,et al.  Neural network-based output-feedback control for stochastic high-order non-linear time-delay systems with application to robot system , 2017 .

[4]  Jinde Cao,et al.  Robust containment tracking of uncertain linear multi-agent systems: a non-smooth control approach , 2014, Int. J. Control.

[5]  Nikolaos Geroliminis,et al.  On the stability of traffic perimeter control in two-region urban cities , 2012 .

[6]  N. Geroliminis,et al.  Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings - eScholarship , 2007 .

[7]  R. Monopoli.  Model reference adaptive control with an augmented error signal , 1974 .

[8]  M. Huifang,et al.  NN approach to state-feedback control of high-order non-linear time-delay systems with time-varying control coefficient , 2018 .

[9]  Jinde Cao,et al.  Distributed robust stabilization of linear multi-agent systems with intermittent control , 2015, J. Frankl. Inst..

[10]  Farzaneh Abdollahi,et al.  Stationary Consensus Control of a Class of High-Order Uncertain Nonlinear Agents With Communication Delays , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[11]  Lin Zhao,et al.  Adaptive Neural Consensus Tracking for Nonlinear Multiagent Systems Using Finite-Time Command Filtered Backstepping , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[12]  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.

[13]  Jack Haddad,et al.  Adaptive perimeter traffic control of urban road networks based on MFD model with time delays , 2016 .

[14]  R. Ortega,et al.  Globally stable adaptive controller for systems with delay , 1988 .

[15]  Markos Papageorgiou,et al.  Exploiting the fundamental diagram of urban networks for feedback-based gating , 2012 .

[16]  A. Bahill.  A simple adaptive Smith-predictor for controlling time-delay systems: A tutorial , 1983, IEEE Control Systems Magazine.

[17]  Carlos F. Daganzo,et al.  Urban Gridlock: Macroscopic Modeling and Mitigation Approaches , 2007 .

[18]  Shengyuan Xu,et al.  New insight into reachable set estimation for uncertain singular time-delay systems , 2018, Appl. Math. Comput..

[19]  N. Geroliminis,et al.  An analytical approximation for the macropscopic fundamental diagram of urban traffic , 2008 .

[20]  Shuzhi Sam Ge,et al.  Neural-Network-Based Switching Formation Tracking Control of Multiagents With Uncertainties in Constrained Space , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[21]  Jack Haddad,et al.  Adaptive multiple input delays compensation under input constraints applied to perimeter traffic control , 2016 .

[22]  Jinde Cao,et al.  Robust fixed-time synchronization of delayed Cohen-Grossberg neural networks , 2016, Neural Networks.

[23]  Jinde Cao,et al.  Master–Slave Synchronization of Heterogeneous Systems Under Scheduling Communication , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[24]  Y. Sugiyama,et al.  Traffic jams without bottlenecks—experimental evidence for the physical mechanism of the formation of a jam , 2008 .

[25]  Nikolas Geroliminis,et al.  Optimal hybrid macroscopic traffic control for urban regions: Perimeter and switching signal plans controllers , 2013, 2013 European Control Conference (ECC).

[26]  Jack Haddad,et al.  Robust perimeter control design for an urban region , 2014 .

[27]  Yuri B. Shtessel,et al.  Adaptive control with asymptotical sliding mode of uncertain plants with input and state delays , 2014, 2014 13th International Workshop on Variable Structure Systems (VSS).

[28]  Nikolas Geroliminis,et al.  Feedback perimeter control for multi-region large-scale congested networks , 2013, 2013 European Control Conference (ECC).

[29]  Yuri B. Shtessel,et al.  Asymptotic sliding mode control approach to adaptive distributed tracking problem for multi-agent nonlinear delayed systems , 2012, Int. J. Control.

[30]  Jinde Cao,et al.  Distributed Observer-Based Cyber-Security Control of Complex Dynamical Networks , 2017, IEEE Transactions on Circuits and Systems I: Regular Papers.

[31]  Nikolaos Geroliminis,et al.  Enhancing model-based feedback perimeter control with data-driven online adaptive optimization , 2017 .