Coupled map car-following model and its delayed-feedback control

Delayed feedback control for chaotic vibration in nonlinear impact dynamics of bouncing agricultural tractor

Agricultural tractors often lose contact and recollide with the ground surface while driving on narrow paddy fields and bumpy farm roads owing to excessive vibrations. These nonlinear impact dynamics can cause chaotic vibrations during tractor operation. Chaotic vibrations are random complex motions that can deteriorate tractor stability and lead to tractor overturning accidents, causing damage to machinery and risk of injury to the operator. This study investigates the theoretical feasibility of chaos control to eliminate chaotic vibrations in tractor dynamics. Delayed feedback (DF) control is employed to eliminate complex vibrations in tractor dynamics. First, the frequency response, bifurcation diagram, and largest Lyapunov exponent are obtained to investigate the nonlinear dynamics of the tractor and identify the parametric region in which chaotic vibrations occur. Subsequently, the DF control is designed based on the trial-and-error method and applied to the tractor dynamics as the driving force control input. The numerical results demonstrate that the DF control can successfully eliminate chaotic vibration and reduce the vibration level. Therefore, this study is expected to contribute to improving the tractor safety by reducing the risk of overturning.

The Car-Following Model and Its Applications in the V2X Environment: A Historical Review

The application of vehicle-to-everything (V2X) technology has resulted in the traffic environment being different from how it was in the past. In the V2X environment, the information perception ability of the driver–vehicle unit is greatly enhanced. With V2X technology, the driver–vehicle unit can obtain a massive amount of traffic information and is able to form a connection and interaction relationship between multiple vehicles and themselves. In the traditional car-following models, only the dual-vehicle interaction relationship between the object vehicle and its preceding vehicle was considered, making these models unable to be employed to describe the car-following behavior in the V2X environment. As one of the core components of traffic flow theory, research on car-following behavior needs to be further developed. First, the development process of the traditional car-following models is briefly reviewed. Second, previous research on the impacts of V2X technology, car-following models in the V2X environment, and the applications of these models, such as the calibration of the model parameters, the analysis of traffic flow characteristics, and the methods that are used to estimate a vehicle’s energy consumption and emissions, are comprehensively reviewed. Finally, the achievements and shortcomings of these studies along with trends that require further exploration are discussed. The results that were determined here can provide a reference for the further development of traffic flow theory, personalized advanced driving assistance systems, and anthropopathic autonomous-driving vehicles.

Stabilization strategies of a general nonlinear car-following model with varying reaction-time delay of the drivers

In this paper, the stabilization strategies of a general nonlinear car-following model with reaction-time delay of the drivers are investigated. The reaction-time delay of the driver is time varying and bounded. By using the Lyapunov stability theory, the sufficient condition for the existence of the state feedback control strategy for the stability of the car-following model is given in the form of linear matrix inequality, under which the traffic jam can be well suppressed with respect to the varying reaction-time delay. Moreover, by considering the external disturbance for the running cars, the robust state feedback control strategy is designed, which ensures robust stability and a smaller prescribed H∞ disturbance attenuation level for the traffic flow. Numerical examples are given to illustrate the effectiveness of the proposed methods.

Controlling traffic jams by time modulating the safety distance

The possibility of controlling traffic dynamics by applying high-frequency time modulation of traffic flow parameters is studied. It is shown that the region of the car density where the uniform (free) flow is unstable changes in the presence of time modulation compared with the unmodulated case. This region shrinks when the speed-up of cars does not exceed some critical value and expands in the opposite case. The flux of the time-modulated flow is an increasing function of the amplitude of the modulation for traffic flows whose density is larger than 1/h where h is the safety distance in the nonmodulated case, while it is a decreasing function in the opposite case. In other words, the safety distance time modulation facilitates car propagation in the case when the mean distance between cars in the congestive traffic is less than h and hinders it when the neighboring cars in the flow are well separated. A link between a microscopic description and the macroscopic fundamental diagram is established.

Delayed feedback control of chaos

Time-delayed feedback control is well known as a practical method for stabilizing unstable periodic orbits embedded in chaotic attractors. The method is based on applying feedback perturbation proportional to the deviation of the current state of the system from its state one period in the past, so that the control signal vanishes when the stabilization of the target orbit is attained. A brief review on experimental implementations, applications for theoretical models and most important modifications of the method is presented. Recent advancements in the theory, as well as an idea of using an unstable degree of freedom in a feedback loop to avoid a well-known topological limitation of the method, are described in detail.

Control of chaos: methods and applications in mechanics

A survey of the field related to control of chaotic systems is presented. Several major branches of research that are discussed are feed-forward ('non-feedback') control (based on periodic excitation of the system), the 'Ott-Grebogi-Yorke method' (based on the linearization of the Poincaré map), the 'Pyragas method' (based on a time-delayed feedback), traditional for control-engineering methods including linear, nonlinear and adaptive control. Other areas of research such as control of distributed (spatio-temporal and delayed) systems, chaotic mixing are outlined. Applications to control of chaotic mechanical systems are discussed.

Effect of adaptive cruise control systems on traffic flow

The flow of traffic composed of vehicles that are equipped with adaptive cruise control (ACC) is studied using simulations. The ACC vehicles are modeled by a linear dynamical equation that has string stability. In platoons of all ACC vehicles, perturbations due to changes in the lead vehicle's velocity do not cause jams. Simulations of merging flows near an onramp show that if the total incoming rate does not exceed the capacity of the single outgoing lane, free flow is maintained. With larger incoming flows, a state closely related to the synchronized flow phase found in manually driven vehicular traffic has been observed. This state, however, should not be considered congested because the flow is maximal for the density. Traffic composed of random sequences of ACC vehicles and manual vehicles has also been studied. At high speeds (approximately 30 m/s ) jamming occurs for concentrations of ACC vehicles of 10% or less. At 20% no jams are formed. The formation of jams is sensitive to the sequence of vehicles (ACC or manual). At lower speeds (approximately 15 m/s ), no critical concentration for complete jam suppression is found. Rather, the average velocity in the pseudojam region increases with increasing ACC concentration. Mixing 50% ACC vehicles randomly with manually driven vehicles on the primary lane in onramp simulations shows only modestly reduced travel times and larger flow rates.

Noise-assisted traffic of spikes through neuronal junctions

The presence of noise, i.e., random fluctuations, in the nervous system raises at least two different questions. First, is there a constructive role noise can play for signal transmission in a neuron channel? Second, what is the advantage of the power spectra observed for the neuron activity to be shaped like 1/f(k)? To address these questions a simple stochastic model for a junction in neural spike traffic channels is presented. Side channel traffic enters main channel traffic depending on the spike rate of the latter one. The main channel traffic itself is triggered by various noise processes such as Poissonian noise or the zero crossings of Gaussian 1/f(k) noise whereas the variation of the exponent k gives rise to a maximum of the overall traffic efficiency. It is shown that the colored noise is superior to the Poissonian and, in certain cases, to deterministic, periodically ordered traffic. Further, if this periodicity itself is modulated by Gaussian noise with different spectral exponents k, then such modulation can lead to noise-assisted traffic as well. The model presented can also be used to consider car traffic at a junction between a main and a side road and to show how randomness can enhance the traffic efficiency in a network. (c) 2001 American Institute of Physics.