Lyapunov stability analysis for a discrete-time lattice hydrodynamic model with steady flow control

2021 ◽  
Author(s):  
Shan Jiang ◽  
Wen-ze Xiong ◽  
Dong-bo Pan ◽  
Yu Zhang ◽  
Geng Zhang
Keyword(s):  
Flow Control ◽  
Steady Flow ◽  
Traffic Flow ◽  
Lyapunov Stability ◽  
Discrete Time ◽  
Control Strategy ◽  
Hydrodynamic Model ◽  
Stable Condition ◽  
Linear Matrix ◽  
Lattice Hydrodynamic Model

This paper put forward a new discrete-time lattice hydrodynamic model with a steady flow control strategy. The controlled discrete-time lattice hydrodynamic model is theoretically studied by the discrete-time Lyapunov stability theory, and a sufficient stable condition to suppress traffic congestion is given in the form of linear matrix inequality. Also, the traffic flow evolution rules under different conditions of control gain are exhibited through numerical simulation, and the stabilization effect of the steady flow control strategy on traffic flow is verified intuitively.

New control strategy for the lattice hydrodynamic model of traffic flow

2017 ◽  
Vol 468 ◽  
pp. 445-453 ◽  
Author(s):  
Chenqiang Zhu ◽  
Shiquan Zhong ◽  
Guangyu Li ◽  
Shoufeng Ma
Keyword(s):  
Traffic Flow ◽  
Control Strategy ◽  
Hydrodynamic Model ◽  
Lattice Hydrodynamic Model

The impact of equilibrium optimal flux deviation on traffic dynamics in lattice hydrodynamic model under V2X environment

2021 ◽  
Author(s):  
Xiaoqin Li ◽  
Guanghan Peng
Keyword(s):  
Traffic Flow ◽  
Hydrodynamic Model ◽  
Stable Condition ◽  
Early Time ◽  
Positive Influence ◽  
Feedback Gain ◽  
Hysteresis Phenomenon ◽  
Lattice Hydrodynamic Model ◽  
The Stability ◽  
The Impact

Abstract In this work, the equilibrium optimal flux deviation is explored as a control signal under V2X environment via traffic modeling of the lattice hydrodynamic model. According to the control theory, the sufficient stable condition can be deduced. In addition, numerical simulation is implemented for the early time impact, the steady-state effect, and the hysteresis phenomenon of traffic flow with the increase of the feedback gain response to the equilibrium optimal flux deviation. The result demonstrates that the equilibrium optimal flux deviation effect has significantly positive influence on the stability of the traffic flow.

Lattice hydrodynamic model for two-lane traffic flow on curved road

2016 ◽  
Vol 85 (3) ◽  
pp. 1423-1443 ◽  
Author(s):  
Jie Zhou ◽  
Zhong-Ke Shi ◽  
Chao-Ping Wang
Keyword(s):  
Traffic Flow ◽  
Hydrodynamic Model ◽  
Lattice Hydrodynamic Model ◽  
Curved Road

Phase transitions in the two-lane density difference lattice hydrodynamic model of traffic flow

2014 ◽  
Vol 77 (3) ◽  
pp. 635-642 ◽  
Author(s):  
Tao Wang ◽  
Ziyou Gao ◽  
Wenyi Zhang ◽  
Jing Zhang ◽  
Shubin Li
Keyword(s):  
Phase Transitions ◽  
Traffic Flow ◽  
Hydrodynamic Model ◽  
Density Difference ◽  
Lattice Hydrodynamic Model

A new two-lane lattice hydrodynamic model on a curved road accounting for the empirical lane-changing rate

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Qingying Wang ◽  
Rongjun Cheng ◽  
Hongxia Ge
Keyword(s):  
Traffic Flow ◽  
Stability Condition ◽  
Hydrodynamic Model ◽  
Neutral Stability ◽  
Lattice Hydrodynamic Model ◽  
Lane Changing ◽  
Content Type ◽  
Curved Road ◽  
The Stability ◽  
Changing Rate

Purpose The purpose of this paper is to explore how curved road and lane-changing rates affect the stability of traffic flow. Design/methodology/approach An extended two-lane lattice hydrodynamic model on a curved road accounting for the empirical lane-changing rate is presented. The linear analysis of the new model is discussed, the stability condition and the neutral stability condition are obtained. Also, the mKdV equation and its solution are proposed through nonlinear analysis, which discusses the stability of the extended model in the unstable region. Furthermore, the results of theoretical analysis are verified by numerical simulation. Findings The empirical lane-changing rate on a curved road is an important factor, which can alleviate traffic congestion. Research limitations/implications This paper does not take into account the factors such as slope, the drivers’ characters and so on in the actual traffic, which will have more or less influence on the stability of traffic flow, so there is still a certain gap with the real traffic environment. Originality/value The curved road and empirical lane-changing rate are researched simultaneously in a two-lane lattice hydrodynamic models in this paper. The improved model can better reflect the actual traffic, which can also provide a theoretical reference for the actual traffic governance.

A novel two-lane lattice hydrodynamic model on a gradient road considering heterogeneous traffic flow

2021 ◽  
pp. 2150340
Author(s):  
Huimin Liu ◽  
Rongjun Cheng ◽  
Hongxia Ge
Keyword(s):  
Numerical Simulation ◽  
Traffic Flow ◽  
Linear Stability ◽  
Hydrodynamic Model ◽  
Heterogeneous Traffic ◽  
Maximum Speed ◽  
Lattice Hydrodynamic Model ◽  
Different Types ◽  
Traffic Flow Stability ◽  
The Stability

In the actual traffic, there are not only cars, but also buses, trucks and other vehicles. These vehicles with different maximum speeds or security headway or both are interspersed irregularly to form a heterogeneous traffic flow. In addition, most of the maximum speed of modern cars is hardly affected by gradients due to the fact that the car engine and brakes are rarely operated at their max while the maximum speed of trucks is affected. Considering that the performance of various types of vehicles is multifarious and the vehicles sometimes drive on the road with slopes, a novel two-lane lattice hydrodynamic model on a gradient road considering heterogeneous traffic flow is proposed in this paper. In order to verify the rationality of the model, the linear stability analysis is carried out first, that is, the linear stability conditions are derived from the linear stability theory and the stability curve is drawn accordingly. The results of the above analysis prove that the three factors studied in this paper, namely, time lane change, slope and mixing of different types of vehicles, all have a significant influence on the stability of traffic flow. The modified Korteweg–de Vries (mKdV) equation is deduced by the nonlinear analysis method, which can describe the propagation characteristics of the traffic density waves near the critical point. Last but not least, the numerical simulation for new model is conducted and the numerical simulation results obtained are in good agreement with theoretical ones. In summary, increasing the lane changing rate or the slope on the uphill can improve the traffic flow stability. What is more, increasing the slope can lower the traffic flow stability on the downhill. Finally, in the heterogeneous traffic flow of different types of vehicles, the vehicles with larger security headway will make traffic flow difficult to stabilize, as do the vehicles with larger maximum speed.

Sign in / Sign up

Export Citation Format

Share Document