Effect of Relative Velocity on the Optimal Velocity Model

In this letter, an improved optimal velocity model was proposed that assumes the effect of relative velocity deceases with the increment of gap between successive cars. Numerical simuation was carried out to test whether this model could depict the braking process correctly. The simuation results show good agreement with observed data.

Improved Car-Following Model Considering Modified Backward Optimal Velocity and Velocity Difference with Backward-Looking Effect

In this paper, a new traffic flow model called the forward-backward velocity difference (FBVD) model based on the full velocity difference model is proposed to investigate the backward-looking effect by applying a modified backward optimal velocity using generalized backward maximum speed. The FBVD model belongs to the family of microscopic models that consider spatiotemporally continuous formulations. Neutral stability conditions of the discrete car-following model are derived using the linear stability theory. The stability analysis results prove that the modified backward optimal velocity has a significant positive effect in stabilizing the traffic flow. Through nonlinear analysis, a kink-antikink solution is derived from the modified Korteweg-de Vries equation of the FBVD model to explain traffic congestion of the model. The validity of this theoretical model is checked using numerical results, according to which traffic jams were found to have been significantly diminished by the introduction of the modified backward optimal velocity.

Velocity anticipation in the optimal velocity model

In this paper, the velocity anticipation in the optimal velocity model （OVM） is investigated. The driver adjusts the velocity of his vehicle by the desired headway, which depends on both instantaneous headway and relative velocity. The effect of relative velocity is measured by a sensitivity function. A specific form of the sensitivity function is supposed and the involved parameters are determined by the both numerical simulation and empirical data. It is shown that inclusion of velocity anticipation enhances the stability of traffic flow. Numerical simulations show a good agreement with empirical data. This model provides a better description of real traffic, including the acceleration process from standing states and the deceleration process approaching a stopped car.

Detailed string stability analysis for bi-directional optimal velocity model

The class of bi-directional optimal velocity models can describe the bi-directional looking effect that usually exists in the reality and is even enhanced with the development of the connected vehicle technologies. Its combined string stability condition can be obtained through the method of the ring-road based string stability analysis. However, the partial string stability about traffic fluctuation propagated backward or forward was neglected, which will be analyzed in detail in this work by the method of transfer function and its H∞ norm from the viewpoint of control theory. Then, through comparing the conditions of combined and partial string stabilities, their relationships can make traffic flow be divided into three distinguishable regions, displaying various combined and partial string stability performance. Finally, the numerical experiments verify the theoretical results and find that the final displaying string stability or instability performance results from the accumulated and offset effects of traffic fluctuations propagated from different directions.

Optimal velocity functions for car-following models

The integral part of the optimal velocity car-following models is the optimal velocity function (OVF), which can be derived from measured velocity-spacing data. This paper discusses several characteristics of the OVF and presents regression analysis on two classical datasets, the Lincoln and Holland tunnels, with different possible OVFs. The numerical simulation of the formation of traffic congestion is conducted with three different heuristic OVFs, demonstrating that these functions give results similar to those of the famous Bando OVF (Bando et al., 1995). Also an alternative method is present for determining the sensitivity and model parameters based on a single car driving to a fixed barrier.

CO_(2) emission control in new CM car-following model with feedback control of the optimal estimation of velocity difference under V2X environment

A new coupled map car-following model in this paper is proposed by considering the influence of the difference of the estimated optimal speed based on the coupled map(CM)car-following model under V2X environment.The stability of the new model is analyzed by applying the control theory,and the conditions are obtained for the stability of the traffic system.And the two scenes of vehicle stopping once and four times have been simulated.The simulation results show that the control term considered with optimal estimation of speed difference can effectively improve the stability of vehicle running and reduce CO_(2) emissions in the CM car-following model.

Re-adhesion control strategy based on the optimal slip velocity seeking method

In the railway industry, re-adhesion control plays an important role in attenuating the slip occurrence due to the low adhesion condition in the wheel-rail inter- action. Braking and traction forces depend on the normal force and adhesion coefficient at the wheel-rail contact area. Due to the restrictions on controlling normal force, the only way to increase the tractive or braking effect is to maximize the adhesion coefficient. Through efficient uti- lization of adhesion, it is also possible to avoid wheel-rail wear and minimize the energy consumption. The adhesion between wheel and rail is a highly nonlinear function of many parameters like environmental conditions, railway vehicle speed and slip velocity. To estimate these unknown parameters accurately is a very hard and competitive challenge. The robust adaptive control strategy presented in this paper is not only able to suppress the wheel slip in time, but also maximize the adhesion utilization perfor- mance after re-adhesion process even if the wheel-rail contact mechanism exhibits significant adhesion uncer- tainties and/or nonlinearities. Using an optimal slip velocity seeking algorithm, the proposed strategy provides a satisfactory slip velocity tracking ability, which was demonstrated able to realize the desired slip velocity without experiencing any instability problem. The control torque of the traction motor was regulated continuously to drive the railway vehicle in the neighborhood of the opti- mal adhesion point and guarantee the best traction capacity after re-adhesion process by making the railway vehicle operate away from the unstable region. The results obtained from the adaptive approach based on the second- order sliding mode observer have been confirmed through theoretical analysis and numerical simulation conducted in MATLAB and Simulink with a full traction model under various wheel-rail conditions.

Effect of multi-velocity-difference in traffic flow

Based on the optimal velocity models, an extended model is proposed, in which multi-veloclty-dllterence aheacl is taken into consideration. The damping effect of the multi-velocity-difference ahead has been investigated by means of analytical and numerical methods. Results indicate that the multi-velocity-difference leads to the enhancement of stability of traffic flow, suppression of the emergence of traffic jamming, and reduction of the energy consumption.

Propulsive Velocity Optimization of 3-Joint Fish Robot Using Genetic-Hill Climbing Algorithm

Underwater robot is a new research field which is emerging quickly in recent years.Previous researches in this field focus on Remotely Operated Vehicles(ROVs),Autonomous Underwater Vehicles(AUVs),underwater manipulators,etc.Fish robot, which is a new type of underwater biomimetic robot,has attracted great attention because of its silence in moving and energy efficiency compared to conventional propeller-oriented propulsive mechanism. However,most of researches on fish robots have been carried out via empirical or experimental approaches,not based on dynamic optimality.In this paper,we proposed an analytical optimization approach which can guarantee the maximum propulsive velocity of fish robot in the given parametric conditions.First,a dynamic model of 3-joint(4 links)carangiform fish robot is derived,using which the influences of parameters of input torque functions,such as amplitude,frequency and phase difference,on its velocity are investigated by simulation.Second,the maximum velocity of the fish robot is optimized by combining Genetic Algorithm(GA)and Hill Climbing Algorithm(HCA).GA is used to generate the initial optimal parameters of the input functions of the system.Then,the parameters are optimized again by HCA to ensure that the final set of parameters is the'near'global optimization.Finally,both simulations and primitive experiments are carried out to prove the feasibility of the proposed method.

Stabilisation analysis of multiple car-following model in traffic flow

An improved multiple car-following model is proposed by considering the arbitrary number of preceding cars, which includes both the headway and the velocity difference of multiple preceding cars. The stability condition of the extended model is obtained by using the linear stability theory. The modified Korteweg-de Vries equation is derived to describe the traffic behaviour near the critical point by applying the nonlinear analysis. Traffic flow can be also divided into three regions： stable metastable and unstable regions. Numerical simulation is in accordance with the analytical result for the model. And numerical simulation shows that the stabilisation of traffic is increasing by considering the information of more leading cars and there is unavoidable effect on traffic flow from the multiple leading cars information.

Multiple car-following model of traffic flow and numerical simulation

On the basis of the full velocity difference （FVD） model, an improved multiple car-following （MCF） model is proposed by taking into account multiple information inputs from preceding vehicles. The linear stability condition of the model is obtained by using the linear stability theory. Through nonlinear analysis, a modified Korteweg-de Vries equation is constructed and solved. The traffic jam can thus be described by the klnk-antikink soliton solution for the mKdV equation. The improvement of this new model over the previous ones lies in the fact that it not only theoretically retains many strong points of the previous ones, but also performs more realistically than others in the dynamical evolution of congestion. Furthermore, numerical simulation of traffic dynamics shows that the proposed model can avoid the disadvantage of negative velocity that occurs at small sensitivity coefficients λ in the FVD model by adjusting the information on the multiple leading vehicles. No collision occurs and no unrealistic deceleration appears in the improved model.

Influence of lane change on stability analysis for two-lane traffic flow

This paper deals mainly with the influence of lane changing behaviours on the stability of two-lane traffic flow under a periodic boundary condition. Following the description of an optimal velocity model for two vehicle groups and the derivation of their stability conditions, the feedback signals, which involve information about vehicles from both lanes acting on the two-lane traffic system, are introduced into the optimal velocity model. The control signals play a role in alleviating the traffic jam only if the traffic state is in congestion, and their role will vanish if the traffic state is in the steady state. The numerical simulations show that lane changing behaviours can break the steady state of two-lane traffic flow and aggravate the traffic disturbance, but the control method would successfully suppress the traffic jam eventually, which implies that the conclusions obtained here have certain theoretical and practical significance.

A control method applied to mixed traffic flow for the coupled-map car-following model

In light of previous work [Phys. Rev. E 60 4000 （1999）], a modified coupled-map car-following model is proposed by considering the headways of two successive vehicles in front of a considered vehicle described by the optimal velocity function. The non-jam conditions are given on the basis of control theory. Through simulation, we find that our model can exhibit a better effect as p = 0.65, which is a parameter in the optimal velocity function. The control scheme, which was proposed by Zhao and Gao, is introduced into the modified model and the feedback gain range is determined. In addition, a modified control method is applied to a mixed traffic system that consists of two types of vehicle. The range of gains is also obtained by theoretical analysis. Comparisons between our method and that of Zhao and Gao are carried out, and the corresponding numerical simulation results demonstrate that the temporal behavior of traffic flow obtained using our method is better than that proposed by Zhao and Gao in mixed traffic systems.

Modified coupled map car-following model and its delayed feedback control scheme

A modified coupled map car-following model is proposed, in which two successive vehicle headways in front of the considering vehicle is incorporated into the optimal velocity function. The steady state under certain conditions is obtained. An error system around the steady state is studied further. Moreover, the condition for the state having no traffic jam is derived. A new control scheme is presented to suppress the traffic jam in the modified coupled map car-following model under the open boundary. A control signal including the velocity differences between the following and the considering vehicles, and between the preceding and the considering vehicles is used. The condition under which the traffic jam can be well suppressed is analysed. The results are compared with that presented by t^onishi et al. （the KKH model）. The simulation results show that the temporal behaviour obtained in our model is better than that in the KKH model. The simulation results are in good agreement with the theoretical analysis.

Modelling of vehicle interaction behavior during discretionary lane-changing preparation process on freeway

In order to increase the accuracy of microscopic traffic flow simulation,two acceleration models are presented to simulate car-following behaviors of the lane-changing vehicle and following putative vehicle during the discretionary lanechanging preparation( DLCP) process, respectively. The proposed acceleration models can reflect vehicle interaction characteristics. Samples used for describing the starting point and the ending point of DLCP are extracted from a real NGSIM vehicle trajectory data set. The acceleration model for a lanechanging vehicle is supposed to be a linear acceleration model.The acceleration model for the following putative vehicle is constructed by referring to the optimal velocity model,in which optimal velocity is defined as a linear function of the velocity of putative leading vehicle. Similar calibration,a hypothesis test and parameter sensitivity analysis were conducted on the acceleration model of the lane-changing vehicle and following putative vehicle,respectively. The validation results of the two proposed models suggest that the training and testing errors are acceptable compared with similar works on calibrations for car following models. The parameter sensitivity analysis shows that the subtle observed error does not lead to severe variations of car-following behaviors of the lane-changing vehicle and following putative vehicle.

A new car-following model with driver's anticipation effect of traffic interruption probability

Traffic interruption phenomena frequently occur with the number of vehicles increasing.To investigate the effect of the traffic interruption probability on traffic flow,a new optimal velocity model is constructed by considering the driver anticipation term in the interruption case for car-following theory.Furthermore,the effect of driver anticipation in the interruption case is investigated via linear stability analysis.Also,the MKdV equation is obtained concerning the effect of driver anticipation in the interruption case.Moreover,numerical simulation states that the driver anticipation term in the interruption case contributes to the stability of traffic flow.

Control strategy of disc braking systems for downward belt conveyors

Reliability of braking systems is a key requirement to ensure the safety of in using downward belt conveyor brakes. By analyzing and comparing three commonly used braking velocity curves, we conclude that the Harrison curve is the best. Given the characteristics of a downward belt conveyor, we studied the control in a closed-loop velocity, a conventional PID method and an optimal PID control method. We used MATLAB/Simulink to simulate the three control methods. Our simulation results show that opti- mal PID control is especially suitable for disc braking systems. To verif!/the results from theoretical anal- ysis and simulation, a multifunctional test-bed was developed to simulate the braking process of a disc brake system. Our experimental results demonstrate that the optimal PID control can make the output velocity to follow a preset velocity correctly with only small fluctuations, meeting the requirements of a flexible brake for a belt conveyor.

A car-following model based on the optimized velocity and its security analysis

An enhanced optimal velocity model(EOVM)that considers driving safety is established to alleviate traffic congestion and ensure driving safety.Time headway is introduced as a criterion for determining whether the car is safe.When the time headway is less discussed to ensure the model's safety and maintain the following state.A stability analysis of the model was carried out to determine than the minimum time headway(TH_(min))or more than the most comfortable time headway(TH_(com)),the acceleration constraints are the stability conditions of the model.The EOVM is compared with the optimal velocity model(OVM)and fuzzy car-following model using the real dataset.Experiments show that the EOVM model has the smallest error in average,maximum and median with the real dataset.To confirm the model's safety,design fleet simulation experiments were conducted for three actual scenarios of starting,stopping and uniform process.

Controlling traffic jams on a two-lane road using delayed-feedback signals

This paper focuses mainly on the stability analysis of two-lane traffic flow with lateral friction,which may be caused by irregular driving behavior or poorly visible road markings,and also attempts to reveal the formation mechanism of traffic jams.Firstly,a two-lane optimal velocity(OV) model without control signals is proposed and its stability condition is obtained from the viewpoint of control theory.Then delayed-feedback control signals composed of distance headway information from both lanes are added to each vehicle and a vehicular control system is designed to suppress the traffic jams.Lane change behaviors are also incorporated into the two-lane OV model and the corresponding information about distance headway and feedback signals is revised.Finally,the results of numerical experiments are shown to verify that when the stability condition is not met,the position disturbances and resulting lane change behaviors do indeed deteriorate traffic performance and cause serious traffic jams.However,once the proper delayed-feedback control signals are implemented,the traffic jams can be suppressed efficiently.

Nonlinear model predictive control with relevance vector regression and particle swarm optimization

In this paper, a nonlinear model predictive control strategy which utilizes a probabilistic sparse kernel learning technique called relevance vector regression （RVR） and particle swarm optimization with controllable random exploration velocity （PSO-CREV） is applied to a catalytic continuous stirred tank reactor （CSTR） process. An accurate reliable nonlinear model is first identified by RVR with a radial basis function （RBF） kernel and then the optimization of control sequence is speeded up by PSO-CREV. Additional stochastic behavior in PSO-CREV is omitted for faster convergence of nonlinear optimization. An improved system performance is guaranteed by an accurate sparse predictive model and an efficient and fast optimization algorithm. To compare the performance, model predictive control （MPC） using a deterministic sparse kernel learning technique called Least squares support vector machines （LS-SVM） regression is done on a CSTR. Relevance vector regression shows improved tracking performance with very less computation time which is much essential for real time control.