Lattice hydrodynamic model-based feedback control method with traffic interruption probability

Mixed traffic system with multiple vehicle types and autonomous vehicle platoon: Modeling, stability analysis and control strategy

In order to reveal the impact of preceding vehicle’s velocity on traffic flow, an extended car-following model considering preceding vehicle’s velocity feedback control is proposed in this paper. The linear stability criterion of the new model is derived through control theory method and it shows that the feedback control signal impacts the stability of traffic flow. Numerical simulation results is in good agreement with the theoretical analysis, which prove that a smaller negative feedback control of the preceding vehicle’s velocity can enhance the stability of traffic flow, while a smaller positive feedback control of the preceding vehicle’s velocity can exacerbate traffic congestion. Moreover, the reaction coefficients of straight and curved road conditions also play an important role in the stability of traffic flow.

In the real traffic, drivers often perceive traffic information with delay time, while presenting asynchronous reactions that form non-constant delay time. Meanwhile, on-ramps are very common in the real traffic network environment, especially on highway sections. Traffic flow merging from the on-ramps has a significant impact on the traffic stability of the main road. Given these facts, we develop an extended lattice hydrodynamic model with drivers’ continuous delay time and on-ramp. Based on the linear and nonlinear stability analysis, we derive the stability criterion and modified Korteweg–de Vries (mKdV) equation of the proposed lattice model; the kink-antikink soliton wave solution obtained by solving the above mKdV equation can be used to describe the propagation and evolution characteristics of density waves near the neutral stable curve. Results show that the ramp inflow ratio and delay time have a significant impact on the stability of traffic flow on the freeway main lane.

Stabilization of traffic flow in optimal velocity model via delayed-feedback control

Nonlinear analysis of a new car-following model accounting for the optimal velocity changes with memory

The first-passage failure of Duffing oscillator with the delayed feedback control under the combined harmonic and white-noise excitations is investigated. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged Ito stochastic differential equations for the system are derived by using the stochastic averaging method. A backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of the first-passage time are established. Finally, the conditional reliability function, the conditional probability density and moments of the first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations with suitable initial and boundary conditions. The effects of time delay in feedback control force on the conditional reliability function, conditional probability density and moments of the first-passage time are analyzed. The validity of the proposed method is confirmed by digital simulation.

The impact of the individual difference on traffic flow under honk environment in lattice hydrodynamic model

Bifurcation analysis of an extended macro model considering time delay and anticipation effect

With cooperative adaptive cruise control vehicles (CACC) development, the heterogeneous traffic flow of human-driven vehicles (HV) and CACC will appear on the same road. Although numerous studies have carefully analyzed the characteristic of the heterogeneous traffic flow, none of them considered the effect of the differences in acceptance of CACC by HV drivers on the heterogeneous traffic flow. In terms of the differences in car-following behaviors of HV drivers with diverse CACC acceptances, this paper deduces the capacity and stability of the heterogeneous traffic flow under different CACC penetration rates. Firstly, the HV driver’s car-following behavior model with different CACC acceptability is calibrated through a questionnaire. Then, the analytical framework of the fundamental diagram and stability of the heterogeneous traffic flow is derived, according to the differences of HV drivers’ acceptance of CACC. Finally, the paper analyzes the influence factors and effects of the heterogeneous traffic flow capacity and stability. The results indicate under different CACC penetration rates, the improvement of HV drivers’ acceptance of CACC increases the capacity and stability of the heterogeneous traffic flow. When CACC penetration rate is lower than 96.35% and HV drivers’ acceptance level of CACC is lower than the critical ratio, the popularity of CACC will decrease the stability of traffic flow. When the penetration rate of CACC is less than 34.76%, and HV drivers’ acceptance level of CACC is lower than the critical proportion, the popularization of CACC will decrease the capacity of heterogeneous traffic.

A modified optimal velocity model is proposed by considering the timid or aggressive characteristics of drivers behavior on traffic flow. The effect of driver’s characteristic on the stability of traffic flow under honk environment is examined through linear stability analysis. It is shown that the parameters related to driver’s characteristics and honk effect all have significant impact on the stability of traffic flow. Precisely, the timid driver is more beneficial to improve the stability of the traffic flow than the aggressive one under honk environment; moreover, the more skillful driver is more advantageous to improve the stability of traffic situation under the same honk environment for the same driver’s characteristics. Finally, many simulation results are found consistent with the theoretical findings which confirm that the drivers characteristics play a significant role on traffic flow dynamics.

In this paper, stability and Hopf bifurcation analysis of a novel hyperchaotic system are investigated. Four feedback control strategies, the linear feedback control method, enhancing feedback control method, speed feedback control method and delayed feedback control method, are used to control the hyperchaotic attractor to unstable equilibrium. Moreover numerical simulations are given to verify the theoretical results.

Based on the fact that the electronic throttle angle effect performs well in the traditional car following model, this paper attempts to introduce the electronic throttle angle into the smart driver model (SDM) as an acceleration feedback control term, and establish an extended smart driver model considering electronic throttle angle changes with memory (ETSDM). In order to show the practicability of the extended model, the next generation simulation (NGSIM) data was used to calibrate and evaluate the extended model and the smart driver model. The calibration results show that, compared with SDM, the simulation value based on the ETSDM is better fitted with the measured data, that is, the extended model can describe the actual traffic situation more accurately. Then, the linear stability analysis of ETSDM was carried out theoretically, and the stability condition was derived. In addition, numerical simulations were explored to show the influence of the electronic throttle angle changes with memory and the driver sensitivity on the stability of traffic flow. The numerical results show that the feedback control term of electronic throttle angle changes with memory can enhance the stability of traffic flow, which shows the feasibility and superiority of the proposed model to a certain extent.

On stabilization of unstable steady states of autonomous ordinary differential equations via delayed feedback controls

Intelligent cruise control systems and traffic flow stability

The delayed feedback control (DFC) methods are noninvasive, which means that the control signal vanishes if the delay time is adjusted to be equal to the period of a target unstable periodic orbit (UPO). If the delay time differs slightly from the UPO period, a nonvanishing periodic control signal is observed. We derive an analytical expression for this period for a general class of multiple-input multiple-output systems controlled by an extended DFC algorithm. Our approach is based on the phase-reduction theory adapted to systems with time delay. The analytical results are supported by numerical simulations of the controlled Rössler system.