String Stability Research Articles

A Kalman-Based Compensation Strategy for Platoons Subject to Data Loss: Numerical and Empirical Study

This article considers a homogeneous platoon with vehicles that communicate through channels prone to data loss. The vehicles use a predecessor-following topology, where each vehicle sends relevant data to the next, and data loss is modeled through a Bernoulli process. To address the lossy communication, we propose a strategy to estimate the missing data based on the Kalman filter with intermittent observations combined with a linear extrapolation stage. This strategy enables the followers to better deal with data dropouts. We compare this approach to one purely based on the linear extrapolation of previous data. The performance of both strategies is analyzed through Monte Carlo simulations and experiments in an ad hoc testbed, considering various data loss and transmission loss probabilities depending on the inter-vehicle distance. The results show that for the considered cases, the proposed strategy outperforms the linear extrapolation approach in terms of tracking and estimation error variances. Our results also show that the proposed strategy can achieve string stability for the mean and variance for both the tracking and estimation errors in scenarios where the basic extrapolation strategy cannot.

Distributed MPC-Based String Stable Platoon Control of Networked Vehicle Systems

In this paper, the string stable platoon control problem of discrete-time networked vehicle systems is considered by using distributed model predictive control (MPC) based method. An optimization problem is established to minimize the cost function associated to the system trajectories. The last-step shifting method is applied to set the local optimal solution as the assumed solution and send it to the neighbor vehicles. By using the sum of the cost function as Lyapunov function, the stability of the closed-loop platoon system is studied. Comparing with existing results, the string stability, which is the unique characteristics of the platoon system, is guaranteed under the bidirectional-based structure as well as the predecessor-follower-based information flow structure. Finally, several simulations are presented to demonstrate the effectiveness of the proposed algorithms.

Longitudinal Control-Oriented Spectrum Sharing Based on C-V2X for Vehicle Platoons

Combined with the development of wireless communication, the vehicle platoon will play a key role in the field of intelligent transportation system, due to its significant advantages in improving traffic safety, increasing road capacity, decreasing energy consumption, etc. In a vehicle platoon, the driving-related information is collected through vehicle-to-vehicle (V2V) communication to guarantee safety and improve control performance. However, it has been proved that the delay and reliability of V2V communication greatly affect the platoon stability. In this article, we investigate the spectrum-sharing problem for a vehicle platoon satisfying longitudinal control requirements. Particularly, we derive the communication delay constraints that guarantee plant stability and string stability. Then, using the obtained delay constraint, the wireless resource management, including the optimal power allocation and selection of spectrum sharing of the involved vehicles, is carried out in consideration of intracell interference and heterogeneous communication requirements. Finally, simulation results demonstrated the feasibility and effectiveness of the proposed scheme in vehicle-following control and wireless resource allocation.

Constant-Spacing Connected Platoons With Robustness to Communication Delays

This paper proposes an approach to make constant-spacing vehicle platoons robust to large delays and loss of communication. It is well known that centralized communication of the desired trajectory is important to simultaneously guarantee both string stability and constant-spacing in platoons. However, the performance of the resulting connected vehicle system (CVS) is vulnerable to large communication delays and communication loss. The main contribution of this work is a new delayed-self-reinforcement-based (DSR-based) approach that approximates the centralized communication based control by a decentralized predecessor follower (PF) control. The resulting blending of centralized communication with the decentralized DSR approach results in predecessor-leader follower (PLF) control with (i) robustness of the convergence to consensus under large communication delays and (ii) substantially-smaller spacing errors under loss of communication. Comparative simulations show that, for the same level of robustness to internal-stability and string-stability, the variation in settling time to consensus for PLF with DSR under large communication delays is 95% less than PLF without DSR and the steady-state error with DSR under loss of communication is 80% less than PLF without DSR.

Lane-Changing Control of Vehicle Platoon Based on OS-ELM Environmental Parameter Identifier

A sliding mode control strategy is presented based on the online sequential extreme learning machine (OS-ELM) environmental parameter identifier. The aim is to eliminate the effects of uncertain environmental parameters in the lane-changing control of the intelligent vehicle platoon. Firstly, the vehicle platoon dynamics model is established considering the communication topology between the vehicle platoon. Then, the vehicle platoon distance error model is obtained based on the constant time distance strategy. Moreover, a sliding mode control strategy based on OS-ELM environmental parameter identifier is proposed to deal with the uncertainty of some environment parameters. Furthermore, finite-time stability and string stability of the system are analyzed by constructing a Lyapunov function. Finally, Carsim/Simulink simulations further verify the effectiveness of the method in this research. The results show that the proposed method estimates the uncertainty parameters accurately in this vehicle platoon. Meanwhile, it guarantees the string stability, and realizes the rapid convergence of errors.

Joint Sliding-Mode Controller and Observer for Vehicle Platoon Subject to Disturbance and Acceleration Failure of Neighboring Vehicles

This article designs a jointly distributed adaptive sliding-mode controller (DASMC) and disturbance observer (DO) for a heterogeneous platoon of connected vehicles (CVs) subject to disturbance and acceleration failure of neighboring vehicles under the multifold common communication topologies. To circumvent the effects of disturbance and acceleration failure of neighboring vehicles, the disturbance arising from the vehicle heterogeneity and nonlinearity as well as the acceleration of neighboring vehicles is jointly estimated as a lumped disturbance by a DO. In particular, the sliding-mode surface with adaptive law is designed based on the defined lumped errors to support the diversity of communication topologies. Then, the DASMC with DO is designed according to the vehicle dynamic model. Meanwhile, the stability of the designed DASMC with DO is analyzed based on the Lyapunov technique. In addition, the string stability of the CV platoon is proved. Finally, the capabilities of the developed control scheme are demonstrated by the simulation and experiment under different communication topologies and compared with existing methods.

Adaptive event-triggered control for almost sure stability for vehicle platooning under interference and stochastic attacks

This paper considers the adaptive event-triggered strategy and controller design of vehicle platooning for stochastic attacks and interferences in communication channels. Bernoulli distribution and Markovian distribution Denial of Service models are introduced in this paper. In designing the controller, Aiming at the stochastic jamming attacks, the stability criterion is presented to guide the controller for almost sure string stability, and meanwhile aiming at the special safety requirements and the reduction of system interferences, the asymmetry event-triggered strategy framework is presented to adapt the transmission environment and the different safety requirements, which is designed to balance the principal concern in different situations. Finally, an example is introduced to demonstrate the controller performances of the vehicle platooning with the Bernoulli distribution and Markovian distribution DoS models, which implies that the presented methods are effective.

String Stable Heterogeneous Aircraft in a Windy Environment

This research develops and analyzes an approach to solve the continuous monitoring problem. The analysis focuses on the string stability of a system of airspeed heterogeneous nonlinear aircraft that are controlled to overfly an endpoint at specified time intervals. The system is modeled as a cascaded set of subsystems where the position of each subsystem, an individual aircraft, is based off the estimated overfly time of the preceding vehicle. The model also includes the effects of steady-state wind and turbulence. The system is made to be string stable by nondimensionalizing a portion of the dynamics, selecting variable command limits, and solving for exponentially stable controller gains. The simulation results confirm the stability guarantees of the theoretical analysis and show that a randomized group of 20 airspeed heterogeneous aircraft experiencing realistic wind and turbulence results in an estimated arrival time error that converges toward a relatively small steady-state range.

Phase and stability of black strings in Einstein-Gauss-Bonnet theory at large D

The phase and stability of black strings in the Einstein-Gauss-Bonnet (EGB) theory are investigated by using the large D effective theory approach. The spacetime metric and thermodynamics are derived up to the next-to-leading order (NLO) in the 1/D expansion. We find that the entropy current defined by the Iyer-Wald formula follows the second law. As in the Einstein theory, the entropy difference from the total mass produces an entropy functional for the effective theory. Including the NLO correction, we find that for the large Gauss-Bonnet coupling constant αGB, the Gregory-Laflamme instability of uniform black strings needs longer wavelength. Moreover, we show that the critical dimension, beyond which non-uiform black strings becomes more stable than uniform ones, increases as αGB becomes large, and approaches to a finite value for αGB→ ∞.

Unified framework for over-damped string stable adaptive cruise control systems

Many recent experiments have shown that the current commercially available adaptive cruise control (ACC) systems demonstrate string instability phenomena. The lower-level time-lag, the sensor time-delay, and the input disturbance primarily contribute to such instability. This paper presents a unified strategy to design ACC systems compensating the lower-level time-lag, the sensor time-delay, and the input disturbance, by fulfilling the over-damped string stability criterion for homogeneous platoons. The over-damped feature associated with string stability explicitly addresses the safety of a platoon in a stricter sense, considering the transient convergence effects, such as over-shoot, under-shoot, and oscillations, and satisfying all the Lp stability norms, where p∈1,∞. In this article, the derived over-damped string-stable strategy compensating lag, delay, and disturbance (OSSCLDD) is presented in a general unified form that applies to any linear or convex velocity-dependent spacing functions. The derived strategy is demonstrated and validated via simulation using a linear constant time gap spacing function and two nonlinear spacing functions, namely, the variable time gap and the quadratic range spacing function.

Memory-Anticipation Strategy to Compensate for Communication and Actuation Delays for Strings-Stable Platooning

Cooperative Adaptive Cruise Control (CACC) has the potential to significantly improve traffic throughput by reducing inter-vehicle following gap. However, communication and actuation delays in CACC systems are detrimental to string stability. A much larger time gap than the lump sum of the two delays is often required for CACC to guarantee string stability, which compromises their benefits on traffic throughput. It remains as a challenge to design string-stable CACC controllers that operate at small time gaps under delays. In this paper, we design a memory-anticipation CACC to explicitly handle communication and actuation delays to fulfill string stability specifications. The proposed controller employs a novel memory-anticipation spacing policy to address communication and actuation delays and is applicable to heterogeneous platoons. Unlike existing CACC controllers, our proposal utilizes past information of the preceding vehicle (i.e. the memory) instead of its current state/control information, which makes the controller robust to communication delay. Furthermore, a Smith predictor (i.e. the anticipation) is designed to compensate for the actuation delay. Both individual vehicle stability and string stability can be guaranteed with the minimum time gap as small as the summation of communication delay and actuation delay. Controller analysis and simulation verify the enhancement of the stability performance with respect to existing studies.

Distributed Trajectory Optimization and Fixed-Time Tracking Control of a Group of Connected Vehicles

This paper investigates a distributed trajectory optimization and trajectory tracking control problem for a collection of vehicles. A two-layered framework is established for distributed trajectory optimization and fixed-time tracking control. The trajectory optimization problem is solved using distributed convex optimization based on spacing errors minimization, resulting in an algorithm to provide the optimal trajectory for all following vehicles. The lower layer plays the role of tracking the designated trajectory and robustly guarantee zero steady-state spacing errors for the vehicular platoon. The controller is derived based on the tracking error system in the context of fixed-time stability and terminal sliding mode control theory. The methodology can guarantee the internal stability and string stability, as demonstrated by numerical simulations.

Eco-Driving of General Mixed Platoons With CAVs and HDVs

Eco-driving has been widely investigated over the last decade, but most studies focused on an individual vehicle or a vehicle platoon consisting of pure connected and automated vehicles (CAVs). Recently, mixed vehicle platoons consisting of both CAVs and human-driven vehicles (HDVs) have attracted much interest, considering the fact that HDVs will mix with CAVs in the traffic system for a long period. This paper proposes an eco-driving strategy for mixed platoons, composing of both offline planning and online tracking. In offline planning, an energy-efficient speed reference and a gearshift reference are determined by using the characteristics of each vehicle and future traffic information through dynamic programming. Offline planning optimised the vehicle speed and gearshift to allow the vehicle powertrain working at a high efficiency region. In online tracking, two different types of model predictive controls (MPCs) are proposed to control the CAVs in real-time. The MPCs are designed to achieve precise speed reference tracking performance and guarantee platoon string stability, respectively. Meanwhile, HDVs within the mixed platoon can be located anywhere in the platoon except working as the first vehicle to improve flexibility. Therefore, the proposed eco-driving strategy is applicable to mixed platoons with more general structures in ordering. The key contribution of this study is that the proposed eco-driving strategy can optimise the total fuel consumption for general mixed platoons. Simulation results show that the proposed eco-driving strategy improves the fuel economy of a mixed platoon by up to 6.39% compared to the benchmark conventional-adaptive cruise control strategies.

Adaptive fuzzy predefined‐time fault‐tolerant control for third‐order heterogeneous vehicular platoon systems

AbstractThis article investigates an adaptive fuzzy predefined‐time fault‐tolerant control problem for third‐order heterogeneous vehicular platoon systems (HVPS) with actuator faults. For the purpose of approximating the unknown nonlinear functions, fuzzy logic systems (FLSs) are used. Because the maximum acceleration changes as a result of actuator faults, a quadratic spacing strategy including fault factor is considered. A predefined‐time fault‐tolerant controller is designed to address the impact of actuator faults. The proposed method makes use of the non‐singular terminal sliding mode control (SMC) approach and predefined time stability criterion. Individual vehicle stability, string stability (SS), and traffic flow stability are all guaranteed in a predefined time. Finally, simulations illustrate the usefulness of the given results.

Leveraging connected vehicle platooning technology to improve the efficiency and effectiveness of train fleeting under moving blocks

This paper leverages emerging highway vehicle platooning technology to improve the efficiency and effectiveness of fleeting trains at minimum headways under moving blocks. The research aims to better understand how closely following trains respond to different throttle and brake control algorithms, and, using insights gained from automobile and truck platooning technology, develop improved train control algorithms balancing fuel efficiency and train headway. To do so, a detailed multi-train performance simulator is developed to evaluate following train control algorithms and then adapt highway vehicle platooning control methods to the heavy haul freight rail domain. Five following train control algorithms under two different communication topologies are formulated to more intelligently consider information on the status of the train ahead when specifying throttle or brake settings for each following train. With string stability, following trains attenuate the actions of preceding trains and each successive train requires less aggressive acceleration and braking rates to maintain headways. The simulation results suggest that certain families of control laws are better than others at managing train separation and fuel consumption within train fleets. The results of this research will allow industry practitioners to develop improved locomotive driver advisory and semi-autonomous adaptive train cruise control systems for the operation of fleets of trains under moving blocks, and railroad operators to make more informed decisions regarding the potential fuel efficiency and capacity benefits of these systems.

Distributed integrated sliding mode control via neural network and disturbance observer for heterogeneous vehicle systems with uncertainties

A distributed sliding mode control based on neural network and disturbance observer is investigated for heterogeneous vehicle systems in this paper. The vehicle systems in this paper consider both parameter uncertainty and disturbance. First, the radial basis function neural network is applied to estimate the parameter uncertainty owing to its universal approximation ability, and the disturbance observer is designed to compensate for the external disturbance. Compared with the existing adaptive methods, the disturbance observer can estimate the external disturbance directly and effectively. Then, constant time headway policy is employed to regulate the inter-vehicle distance and improve the string stability. Unlike most existing sliding mode control strategy for vehicle platoons, the string stability is achieved via employing sufficient conditions on the control parameters rather than employing coupled sliding mode control. Afterward, modified constant time headway policy is designed to reduce the effect of nonzero initial inter-vehicle spacing and improve the traffic density. Finally, the simulation results with constant time headway policy and modified constant time headway policy are provided to demonstrate the effectiveness and advantages of the proposed approaches.

Hybrid Cost Function Distributed MPC for Vehicle Platoons With Stability and String Stability Properties

Distributed MPC schemes for control of vehicle platoons typically employ a p-norms based cost function to achieve stability and string stability. Quadratic cost functions yield smoother trajectories, but they are not aligned with string stability conditions. Hence, in this paper, we develop distributed MPC controllers for vehicle platoons based on a hybrid cost function, which combines infinity norms and quadratic forms. Sufficient conditions for global platoon stability and leader-follower string stability are derived for the developed hybrid cost function and applied to lateral dynamics control. Simulation results show that the hybrid cost function yields lateral position errors that are 10 times smaller (for the maximum error) compared with an infinity norms based cost function.

Implicit Lyapunov Function-based Formation Control for Heterogeneous Vehicular Platoons with Time Delays

In order to lower the drivers’ driving pressure and improve traffic efficiency, academic and industrial interest in the cooperative adaptive cruise control (CACC) system has been substantial. In this research, we use the Implicit Lyapunov Function (ILF) technique to develop a switching controller for HVPs with temporal delays. The constant time headway strategy is utilized to construct the HVPs error model first. Then, the implicit Lyapunov function is used to develop the switching controller. Finally, the conditions of internal stability and string stability are obtained. The suggested switching controller has been shown to maintain internal and string stability in simulations involving heterogeneous vehicle platoons.

Development of Connected and Automated Vehicle Platoons With Combined Spacing Policy

Vehicle platoon has the potential to significantly improve traffic throughput and reduce fuel consumption and emissions and thus has attracted extensive attention recently. In this study, we propose a vehicle platoon of connected and automated vehicles (CAVs) with a combined spacing policy to enhance traffic performance. First, a combined spacing policy composed of the constant time gap (CTG) and constant spacing (CS) is formulated for the proposed vehicle platoon, where the leader adopts the CTG and the followers use the CS policy. Based on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$h_{2}$ </tex-math></inline-formula> -norm string stability criteria, the notion of exogenous-head-to-tail string stability is newly introduced, and the sufficient conditions of the local stability and string stability in the frequency domain are derived using the Routh-Hurwitz criterion and Laplace transform respectively. Numerical experiments are conducted to validate the string stability. The effectiveness of the proposed vehicle platoons is verified by theoretical analysis and numerical experiments using two typical scenarios and several measurements of effectiveness (MOE) in various performance aspects, including efficiency, safety, energy, and emission. The results show that the proposed vehicle platoon performs better than the CS-based vehicle platoon in all aspects except for efficiency. It also indicates that the proposed vehicle platoon has obvious advantages over the CTG-based vehicle platoon in efficiency and safety aspects. The findings have demonstrated the merits of the combined application of CTG and CS policies for the vehicle platoon in enhancing stability and traffic performance.

A New Topology for Homogeneous Vehicular Platoon under Disturbances

Vehicle platooning has attracted a lot of interest in research in the last decade as it introduced a solution to many problems in traffic flow, safety, fuel economy, and reducing CO2 emissions. As the cost reduction is crucial and necessary to the business’s sector, in this paper, communication cost reduction is achieved via proposing a new topology called Bidirectional Odd Leader (BDOL). The BDOL topology is advantageous in terms of cost compared to the BDL topology due to the BDOL is a relaxation of the BDL topology. The string stability of the dynamical system with the proposed topology is first proven through numerical comparison with BDL topology. Then, the performance of the proposed topology has been evaluated by intensive computer-based simulation. A homogeneous platoon consisting of eight vehicles is created and tested on a straight and curved track, while keeping a small desired inter-vehicle distance. We evaluated the performance of our topology, and tested the string stability in many scenarios. These scenarios include platoon moving on a straight track with or without disturbance, lastly a velocity disturbance produced by a curved track affecting the platoon is also investigated. The results demonstrate the effectiveness of the proposed topology in achieving the intended objectives.