Analysis of a modified two-lane lattice model by considering the density difference effect

In this paper, a modified lattice hydrodynamic model of traffic flow is proposed by considering the density difference between leading and following lattice for two-lane system. The effect of density difference on the stability of traffic flow is examined through linear stability analysis and shown that the density difference term can significantly enlarge the stability region on the phase diagram. To describe the phase transition of traffic flow, the Burgers equation and mKdV equation near the critical point are derived through nonlinear analysis. To verify the theoretical findings, numerical simulation is conducted which confirms that traffic jam can be suppressed efficiently by considering the density difference effect in the modified lattice model for two-lane traffic.     

A new lattice model of two-lane traffic flow with the consideration of optimal current difference

In this paper, a new lattice model of traffic flow is proposed with the consideration of the optimal current difference for two-lane system. The linear stability condition is derived through linear stability analysis, which shows that the optimal current difference term can improve the stability of traffic flow. The mKdV equation is obtained through nonlinear analysis. Thus the space of traffic flow is divided into three regions: the stable region, the metastable region and the unstable region respectively. Moreover, numerical simulation confirms that the traffic jam can be suppressed efficiently by considering the optimal current difference effect in extended lattice model of two-lane traffic flow.     

离散交通流模型的反馈线性化与拥堵控制

在自动化高速公路环境下,提出一种改进的宏观离散交通流模型密度控制方法.利用反馈线性化方法,将宏观离散交通流模型转换为一般容易处理的线性系统模型,简化了密度控制器的设计.利用线性系统中具有输入变换的跟踪反馈控制方法,对线性化后的系统模型设计控制律.通过控制该线性系统的状态变量,间接稳定离散交通流模型中的交通流密度,达到对道路交通流拥堵的控制.同时给出设计方法和步骤,仿真实例说明了方法的实用性.     

Instability of cooperative adaptive cruise control traffic flow: A macroscopic approach

This paper proposes a macroscopic model to describe the operations of cooperative adaptive cruise control (CACC) traffic flow, which is an extension of adaptive cruise control (ACC) traffic flow. In CACC traffic flow a vehicle can exchange information with many preceding vehicles through wireless communication. Due to such communication the CACC vehicle can follow its leader at a closer distance than the ACC vehicle. The stability diagrams are constructed from the developed model based on the linear and nonlinear stability method for a certain model parameter set. It is found analytically that CACC vehicles enhance the stabilization of traffic flow with respect to both small and large perturbations compared to ACC vehicles. Numerical simulation is carried out to support our analytical findings. Based on the nonlinear stability analysis, we will show analytically and numerically that the CACC system better improves the dynamic equilibrium capacity over the ACC system. We have argued that in parallel to microscopic models for CACC traffic flow, the newly developed macroscopic will provide a complete insight into the dynamics of intelligent traffic flow.     

A new car-following model with consideration of the prevision driving behavior

In the paper, a new car-following model is presented with the consideration of the prevision driving behavior on a single-lane road. The model’s linear stability condition is obtained by applying the linear stability theory. And through nonlinear analysis, a modified Korteweg–de Vries (mKdV) equation is derived to describe the propagating behavior of traffic density wave near the critical point. Numerical simulation shows that the new model can improve the stability of traffic flow by adjusting the driver’s prevision intensity parameter, which is consistent with the theoretical analysis.     

Payne-Whitham型宏观交通流模型波动特性

宏观交通流模型将交通流比拟成流体流,通过整体变量如交通流量、平均车速以及交通密度来研究其整体性质,得到了越来越多的肯定.文章采用波前展开的方法,研究Payne-Whitham型宏观交通流模型描述扰动沿交通流波动的特性,同时给出了相应的稳定性条件.最后利用Padé逼近法进行数值仿真,得到的结果与理论分析相一致.     

Lattice hydrodynamic model of pedestrian flow considering the asymmetric effect

The original lattice hydrodynamic model of traffic flow is extended to single-file pedestrian movement at middle and high density by considering asymmetric interaction (i.e., attractive force and repulsive force). A new optimal velocity function is introduced to depict the complex behaviors of pedestrian movement. The stability condition of this model is obtained by using the linear stability theory. It is shown that the modified optimal velocity function has a remarkable influence on the neutral stability curve and the pedestrian phase transitions. The modified Korteweg-de Vries (mKdV) equation near the critical point is derived by applying the reductive perturbation method, and its kink-antikink soliton solution can better describe the stop-and-go phenomenon of pedestrian flow. From the density profiles, it can be found that the asymmetric interaction is more efficient than the symmetric interaction in suppressing the pedestrian jam. The numerical results are consistent with the theoretical analysis.     

Dynamical behavior in a stage-structured differential-algebraic prey-predator model with discrete time delay and harvesting

A differential-algebraic model system which considers a prey-predator system with stage structure for prey and harvest effort on predator is proposed. By using the differential-algebraic system theory and bifurcation theory, dynamic behavior of the proposed model system with and without discrete time delay is investigated. Local stability analysis of the model system without discrete time delay reveals that there is a phenomenon of singularity induced bifurcation due to variation of the economic interest of harvesting, and a state feedback controller is designed to stabilize the proposed model system at the interior equilibrium; Furthermore, local stability of the model system with discrete time delay is studied. It reveals that the discrete time delay has a destabilizing effect in the population dynamics, and a phenomenon of Hopf bifurcation occurs as the discrete time delay increases through a certain threshold. Finally, numerical simulations are carried out to show the consistency with theoretical analysis obtained in this paper.     

Controller design for stabilizing bilinear systems with state-based switching

Some nonlinear systems can be approximated by switching bilinear systems. In this paper, we proposed a method to design state-based stabilizing controller for switching bilinear systems. Based on the similarity between switching bilinear systems and switching linear systems, corresponding switching linear systems are obtained for switching bilinear systems by applying state-based feedback control laws. Instead, we consider asymptotically stabilizing the corresponding switching linear system through solving a number of relaxed LMI conditions. Stabilizing controllers for switching bilinear systems can be derived based on the results of the corresponding switching linear systems. The stability of the controller is proved step by step through the decreasing of the multiple Lyapunov functions along the state trajectory. The effectiveness of the method is demonstrated by both a theoretical example and an example of urban traffic network with traffic signals.     

Bifurcation,chaos, and their control in a wheelset model

In this paper, we present an improved wheelset motion model with two degrees of freedom and study the dynamic behaviors of the system including the symmetry, the existence and uniqueness of the solution, continuous dependence on initial conditions, and Hopf bifurcation. The dynamic characteristics of the wheelset motion system under a nonholonomic constraint are investigated. These results generalize and improve some known results about the wheelset motion system. Meanwhile, based on multiple equilibrium analysis, calculation of Lyapunov exponents and Poincaré section, the chaotic behaviors of the wheelset system are discussed, which indicates that there are more complex dynamic behaviors in the railway wheelset system with higher order terms of Taylor series of trigonometric functions. This paper has also realized the chaos control and bifurcation control for the wheelset motion system by adaptive feedback control method and linear feedback control. The results show that the chaotic wheelset system and bifurcation wheelset system are all well controlled, whether by controlling the yaw angle and the lateral displacement or only by controlling the yaw angle. Numerical simulations are carried out to further verify theoretical analyses.     

用负的状态反馈量控制和同步Lorenz系统

本文研究了Lorenz系统的控制与同步问题.利用负状态反馈的方法和Lyapunov稳定性理论,得到了能保证系统渐近稳定和同步的有关反馈增益的一些充分条件.最后,数值实验证实了理论分析的结果.     

A modified coupled map car following model and its traffic congestion analysis

Based on the coupled map car following model which was presented by Konishi et al. [Konishi KJ, Kokame H, Hirate K. Phys Rev E 1999;60:4000-7.] (for short, KKH), a modified coupled map car following model is proposed. In this model two successive vehicles’ headway distances in front of the considered one are incorporated in the optimal velocity (for short, OV) function. The stability condition is given for the change of the speed of the preceding vehicle on the base of the control theory. The control scheme in KKH model is applied to the modified model and the feedback gains are determined. Comparison between the modified model and KKH model is carried out. And the corresponding numerical simulation results show that the temporal behavior obtained by our model is better than that by KKH model. The simulation results are in good agreement with the theoretical analysis.     

Numerical time-delayed feedback control in a neural network with delay

In this article, by a nonstandard finite-difference method we obtain the general time delayed feedback control numerical discrete scheme for a delayed neural network model. Firstly, the local stability of the equilibria point is discussed according to the Neimark–Sacker bifurcation theory. Then, from the point of view of control, for any step-size, a general time delayed feedback control numerical algorithm is introduced to delay the onset of the Neimark–Sacker bifurcation at a desired point by choosing appropriate control parameters. This controller can deal with the general system that the natural equilibrium cannot be given by analytic expression. Finally, numerical examples are provided to illustrate the theoretical results. The results show that the time delayed feedback numerical scheme is better than a polynomial function time delayed feedback method.     

When does a T-junction require a left-turn lane?

A four-state, ergodic Markov chain is used to model a T-junction on a narrow, two-lane, major road. The states are defined more realistically than by previous authors. A formula is obtained for the proportion of traffic configurations in which cars travelling one way are brought to a halt by those turning left onto the minor road. This formula is obtained as a function of four parameters: the mean traffic flows in each direction, the probability that a car on the major road will turn left at the junction and the minimum time gap, in the oncoming flow of traffic, which that manouevre requires. If this proportion is higher than is deemed acceptable, then a left-turn is needed.     

Kink–antikink density wave of an extended car-following model in a cooperative driving system

We propose an extended optimal velocity model applicable to cooperative driving control system by considering the headway of arbitrary number of cars that precede and the relative velocity. The stability condition of the extended model is obtained by using the linear stability theory. The modified Korteweg-de Vries (mKdV) equation is derived to describe the traffic behavior near the critical point by applying the nonlinear analysis. Thus the traffic jams can be described by the kink–antikink density wave which is the solution of the mKdV equation. The simulation results confirm the analytical results and show that the traffic jams are suppressed more efficiently with considering not only the headway of more vehicles ahead but also the relative velocity.     

道路维修施工路段交通分流信控优化模型

针对道路维修施工期间常采用的部分路面封闭施工且利用辅路进行分流的情形,探讨了交通分流信控优化模型。借助交通流波动理论,分析了施工路段及其前后车流拥挤排队及疏散特征和规律,分析了对车流进行控制需满足的约束,并分析了车流的延误计算公式。以总的车辆行驶时间最小化目标,原路径及分流路径的绿时分配及信号周期为优化参数,考虑交通分流控制的各种约束,建立了道路施工路段交通分流信控优化模型。分析了该模型属于非凸问题,因此提出了一种近似求解最优解的办法。通过一个示例对模型和求解算法进行了验证,并对一些规律性结果进行了分析。     

Analytical studies on the instabilities of heterogeneous intelligent traffic flow

It has been widely reported in literature that a small perturbation in traffic flow such as a sudden deceleration of a vehicle could lead to the formation of traffic jams without a clear bottleneck. These traffic jams are usually related to instabilities in traffic flow. The applications of intelligent traffic systems are a potential solution to reduce the amplitude or to eliminate the formation of such traffic instabilities. A lot of research has been conducted to theoretically study the effect of intelligent vehicles, for example adaptive cruise control vehicles, using either computer simulation or analytical method. However, most current analytical research has only applied to single class traffic flow. To this end, the main topic of this paper is to perform a linear stability analysis to find the stability threshold of heterogeneous traffic flow using microscopic models, particularly the effect of intelligent vehicles on heterogeneous (or multi-class) traffic flow instabilities. The analytical results will show how intelligent vehicle percentages affect the stability of multi-class traffic flow.     

Nonlinear modelling of the interaction between phytoplankton and zooplankton with the impulsive feedback control

In this paper, a mathematical model including the phytoplankton and zooplankton with the impulsive feedback control is presented. The sufficient conditions for the existence of the order-1 and order-2 periodic solutions are obtained by using the geometrical theory of semi-continuous dynamic system. The stability of the order-1 periodic solution is discussed by the analogue of the Poincaré criterion. Finally, our results are justified by the numerical simulations.     

Stability switches and bifurcation in a two-degrees-of-freedom nonlinear quarter-car with small time-delayed feedback control

In this paper, we investigate a two-degrees-of-freedom nonlinear quarter-car model with time-delayed feedback control. It is well known that a time delay has destabilizing effects in mathematical models. However, delays are not necessarily destabilizing. In this work we explore a system where a time delay can be both stabilizing and destabilizing. Using the generalized Sturm criterion, the critical control gain for the delay-independent stability region and critical time delays for stability switches are derived. It is shown that there is a small parameter region for delay-independently stability of the system. Once the controlled system with time delay is not delay-independently stable, the system may undergo stability switches with the variation of the time delay. These stability switches correspond to Hopf bifurcations that occur when the time delays cross critical values. Properties of Hopf bifurcation such as direction and stability of bifurcating periodic solutions are determined by using the normal form theory and centre manifold theorem. Numerical simulations are provided to support the theoretical analysis. The critical conditions can provide a theoretical guidance for the design of vehicles with significant reduction of vibration in order to increase passengers ride comfort.     

Optimal control laws for traffic flow

Optimal “on–off” laws for the traffic signals are developed based on the bilinear control problem with the binary constraints. A Lyapunov function based feedback law for regulating traffic congestions is developed. Also, a real-time optimal signal law is developed using a novel binary optimization method. Both methods are tested and compared, and our tests demonstrate that the both methods provide very effective and efficient traffic control laws.