Achieve String Stability Research Articles

On disturbance propagation in vehicular platoons with different communication ranges

In the control of vehicular platoons, the disturbances acting on one vehicle can propagate and affect other vehicles. If the disturbances do not amplify along the vehicular string, then it is called string stable. However, it is usually difficult to achieve string stability with a distributed control setting, especially when a constant spacing policy is considered. This note considers the string unstable cases and studies disturbance propagation in a nonlinear vehicular platoon consisting of n+1 vehicles where the (virtual) leading vehicle provides the reference for a constant spacing policy. Apart from the communications between consecutive vehicles, we also assume that each vehicle can receive information from r neighbors ahead, that is, the vehicular platoon has communication range r. Inspired by existing control protocols, a unified distributed nonlinear control law with a variable r is proposed to facilitate the analysis. For the maximal overshoot of the inter-vehicular spacing errors, we explicitly show that the effect of disturbances, including the external disturbances acting on each vehicle and the acceleration of the leading vehicle, is scaled by O(nr) for a fixed n. This implies that disturbance propagation can be reduced by increasing communication range. Numerical simulation is provided to illustrate the main results.

Betweenness centrality can inform stability and delay margin in a large-scale connected vehicle system

Delays in information transmission and human reactions act as one main factor of instability in connected vehicle networks (CVN). This study reveals that a relationship exists between the delay margin (DM) of a class of CVN and betweenness centrality (BC) associated with the network graph of this CVN. Two dynamic models are considered, one only uses velocity information of vehicles while the other considers velocity and headway to regulate vehicles’ motions. We randomize vehicle orders in multiple trials to generate platoon samples. DM and BC values are computed in each platoon and the respective statistical models between them are obtained. The results show that the mean and variance of BC have a negative correlation with DM. We complete the study with a string stability analysis, which demonstrates the diffusion of oscillations in a platoon where there is no explicit leader. In summary, the work bridges DM with BC in a CVN and provides insights toward designing platoons with larger DM. These rules also enable means to rapidly estimate DM from statistical models. Lastly, we report that, to achieve string stability, large human-driven vehicle clusters are not recommended.

Safety-critical traffic control by connected automated vehicles

Connected automated vehicles (CAVs) have shown great potential in improving traffic throughput and stability. Although various longitudinal control strategies have been developed for CAVs to achieve string stability in mixed-autonomy traffic systems, the potential impact of these controllers on safety has not yet been fully addressed. This paper proposes safety-critical traffic control (STC) by CAVs—a strategy that allows a CAV to maintain safety relative to both the preceding vehicle and the following human-driven vehicles (HVs). Specifically, we utilize control barrier functions (CBFs) to impart collision-free behavior with formal safety guarantees to the closed-loop system. The safety of both the CAV and HVs is incorporated into the framework through a quadratic program-based controller that minimizes deviation from a nominal stabilizing traffic controller subject to CBF-based safety constraints. Considering that some state information of the following HVs may be unavailable to the CAV, we employ state observer-based CBFs for STC. Finally, we conduct extensive numerical simulations – that include vehicle trajectories from real data – to demonstrate the efficacy of the proposed approach in achieving provably safe traffic.

On Structural and Safety Properties of Head-to-Tail String Stability in Mixed Platoons

The interaction between automated and human-driven vehicles in mixed (human/automated) platoons is far from understood. To study this interaction, the notion of head-to-tail string stability was proposed in the literature. Head-to-tail string stability is an extension of the standard string stability concept where, instead of asking every vehicle to achieve string stability, a lack of string stability is allowed due to human drivers, provided it can be suitably compensated by automated vehicles sparsely inserted in the platoon. This work introduces a theoretical framework for the problem of head-to-tail string stability of mixed platoons: it discusses a suitable vehicle-following human driver model to study mixed platoons, and it gives a reduced-order design strategy for head-to-tail string stability only depending on three gains. The work further discusses the safety limitations of the head-to-tail string stability notion, and it shows that safety improvements can be attained by an appropriate reduced-order design strategy only depending on two additional gains. To validate the effectiveness of the design, linear and nonlinear simulations show that the string stability/safety trade-offs of the proposed reduced-order design are comparable with those resulting from full-order designs.

Cooperative control of a platoon of connected autonomous vehicles and unconnected human‐driven vehicles

AbstractBy using kinematic state information obtained through vehicle‐to‐vehicle communications, connected autonomous vehicles (CAVs) can drive cooperatively to alleviate shockwave propagation associated with traffic disturbances. However, during the transition to full autonomy, CAVs and human‐driven vehicles (HDVs) will coexist on the road, creating mixed‐flow traffic. The inherent heterogeneity and randomness in human driving behavior can generate additional disturbances in the traffic flow. Further, HDVs without communication functionality (unconnected HDVs) can cause the control performance of CAVs to degrade by negatively impacting platoon formation. To proactively mitigate the negative impacts of HDVs in mixed‐flow traffic, this study proposes a cooperative control strategy with three components for platoons consisting of CAVs and unconnected HDVs: (i) a number estimator for estimating the number of HDVs between two CAVs, (ii) a kinematic state predictor for predicting the kinematic states of HDVs, and (iii) a multi‐anticipative car‐following controller (i.e., control strategy using kinematic state information of multiple preceding vehicles) for CAVs to maintain string stability and desired time headway. To initialize the proposed strategy, the number estimator is developed using a deep neural network (DNN). Then, a DNN‐based kinematic state predictor predicts the kinematic states of HDVs for CAVs to enable multi‐anticipative car‐following control. The multi‐anticipative car‐following controller is implemented using an extended intelligent driver model‐guided deep deterministic policy gradient algorithm, which ensures safety, string stability, and traffic efficiency. The effectiveness of the proposed control strategy is validated through numerical experiments using NGSIM data. Results indicate that the proposed strategy can produce accurate estimations of the number and the kinematic states of HDVs between CAVs. Further, it can achieve string stability while maintaining smaller time headways, compared to car‐following models used for training guidance under different market penetration rates of CAVs, which significantly improves traffic smoothness and mobility.

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.

A Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

Cooperative Adaptive Cruise Control (CACC) is considered as a key potential enabler to improve driving safety and traffic efficiency. It allows for automated vehicle following using wireless communication in addition to onboard sensors. To achieve string stability in CACC platoons, constant time gap (CTG) spacing policies have prevailed in research; namely, vehicle interspacing grows with the speed. While constant distance gap (CDG) spacing policies provide superior potential to increase traffic capacity than CTG, their major drawbacks are a smaller safety margin at high velocities and that string stability cannot be achieved using a one-vehicle look-ahead communication. In this work, we propose to apply CDG only in a few driving situations, when traffic throughput is of highest importance and safety requirements can be met due to relatively low velocities. As the most relevant situations where CDG could be applied, we identify starting platoons at signalized intersections. With this application scenario we show that applying CDG only in a few specific and crucial situation can have a major impact on traffic efficiency. Specifically, we compare CTG with CDG regarding its potential to increase the capacity of traffic lights. Starting with the elementary situation of single traffic lights we expand our scope to whole traffic networks including several thousand vehicles in simulation. Using real world data to calibrate and validate vehicle dynamics simulation and traffic simulation, the study discusses the most relevant working parameters of CDG, CTG, and the traffic system in which both are applied.

Event-triggered control of vehicle platoon under deception attacks

This paper addresses the issue of control of a vehicle platoon system with limited on-board energy and communication resources and subjected to cyber-physical attacks. A platoon model for the predecessor-leader following topology under the effect of cyber-attack and time-varying delay is developed. A stochastic type deception attack is considered in this paper at the sensor-controller end of a vehicle. The probability of occurrence of attack is represented using a random variable. In addition, to reduce the usage of resources in a system, a decentralized event-triggering communication mechanism is proposed where each vehicle can decide independently on when to transmit its state to the controller. Further, the criteria for co-designing of control law and triggering parameter ensuring internal stability of the platoon system is developed based on the proposed triggering mechanism. A condition to achieve string stability for the controller is also obtained. Further, to avoid the problem of Zeno phenomena, a lower bound on the transmission period is presented. The effectiveness of the proposed methodology is established through simulation example.

Prescribed Performance Concurrent Control of Connected Vehicles With Nonlinear Third-Order Dynamics

Transient performance (e.g., convergence rate and overshoot of spacing errors) is essential for cooperative driving of connected vehicles but was rarely studied. This paper investigates a prescribed performance concurrent control (PPCC) strategy for vehicular platooning systems with consideration of unknown parameters, disturbances and actuator saturation. First, a new spacing policy is considered to achieve string stability and improve the road capacity under virtual leader-bidirectional information flow. Then, to facilitate the controller design without the sign limitations of initial tracking errors (ITEs), a new transformed error function (TEF) is designed. Based on this, PPCC is employed for both individual vehicle stability and string stability directly. Subsequently, distributed adaptive low complexity tracking controllers via sliding mode control method are developed, which can guarantee that all the involved closed-loop signals are uniformly ultimately bounded. Moreover, an auxiliary system is introduced to tackle the effect of actuator saturation. Finally, numerical simulation examples and results are conducted to illustrate the effectiveness and efficiency of the proposed platoon control methods.

Toward a Comprehensive Impossibility Result for String Stability

We provide a comprehensive impossibility result toward achieving string stability, i.e., keeping local relative errors in check with local controllers independently of the size of a chain of subsystems. We significantly extend the existing results, from the linear time-invariant (LTI) setting to any homogeneous controllers that can be nonlinear, time varying, and locally communicating. We prove this impossibility for a set of definitions with various norm choices, including the $L_2$ -type standard and a bounded-input implies bounded-output (BIBO) type criterion. All the results hold for a general discrete-time controller, which should cover most applications.

Adaptive Neuro-Fuzzy Predictor-Based Control for Cooperative Adaptive Cruise Control System

In this paper, an adaptive neuro-fuzzy predictor-based control (ANFPC) approach with integrated automotive radar and vehicle-to-vehicle (V2V) communication for the design of the cooperative adaptive cruise control (CACC) system is presented, which concerns not only the safety and riding comfort of a vehicle but also enhances its fuel efficiency. This paper consists of two main parts: preceding vehicle state estimation and following vehicle controller. First, the prospective information of the preceding vehicle, such as position, velocity, and acceleration, can be derived through radar sensor, and the control force of the preceding vehicle can be transmitted to the following vehicles through V2V communication. A Takagi–Sugeno fuzzy model is then utilized to estimate the preceding vehicle model, and the predicted state sequence of the preceding vehicle can be obtained. Second, based on these predicted data, the following vehicle is controlled by the proposed ANFPC scheme to maintain each vehicle within the desired distance headway and thus achieve string stability of vehicle platooning and fuel efficiency. The experimental results on the CarSim environment show that the proposed control strategy for the CACC system can significantly reduce the fuel consumption while ensuring driving comfort and safety.

Event-Driven Connected Vehicular Platoon Control With Mixed Time-Varying Delay

In this research, connected vehicular platoon control is investigated with mixed time-varying delay. An event-driven information interaction method for connected vehicular platoon system is built, which considered the combined effect of communication-actuator time-varying delay and event-driven mechanism. The new standard for asymptotically stable and criterion for the controller gains and the trigger parameters are obtained based on Lyapunov method. The derived controller is offset by new conditions, which are used to ensure the vehicular platoon system that can achieve string stability. Finally, the effectiveness and advantage of the proposed algorithm are demonstrated by numerical simulations and experiments results with electric experimental cars.

An Adaptive Switched Control Approach to Heterogeneous Platooning With Intervehicle Communication Losses

The advances in distributed intervehicle communication networks have stimulated a fruitful line of research in cooperative adaptive cruise control (CACC). In CACC, individual vehicles, grouped into platoons, must automatically adjust their own speed using on-board sensors and communication with the preceding vehicle so as to maintain a safe intervehicle distance. However, a crucial limitation of the state of the art of this control scheme is that the string stability of the platoon can be proven only when the vehicles in the platoon have identical driveline dynamics and perfect engine performance (homogeneous platoon), and possibly an ideal communication channel. This paper proposes a novel CACC strategy that overcomes the homogeneity assumption and that is able to adapt its action and achieve string stability even for uncertain heterogeneous platoons. Furthermore, in order to handle the inevitable communication losses, we formulate an extended average dwell-time framework and design an adaptive switched control strategy, which activates an augmented CACC or an augmented adaptive cruise control strategy depending on communication reliability. Stability is proven analytically and simulations are conducted to validate the theoretical analysis.

Vehicular platoons in cyclic interconnections

Vehicle platooning has received considerable attention as a means to achieve more efficient transportation networks and vehicle autonomy. It is well known that certain systems experience undesired behaviours (instability and string instability) when the length of the platoon grows. In this context, we study homogeneous platoons of vehicles with linear dynamic models, having bi-directional communication and maintaining a constant (velocity independent) target inter vehicle spacing. We investigate both stability and string instability if the string length increases, where the vehicles utilise weighted information from multiple vehicles ahead and behind. We find conditions for the weighting factors and the linear systems that are necessary for stability of long platoons. We then show that by selecting a communication range that increases linearly with the platoon size, it is possible to achieve string stability in some cases. Further, we show that careful selection of the weighting factors can reduce the disturbance amplification considerably.

An Adaptive Approach to Cooperative Longitudinal Platooning of Heterogeneous Vehicles with Communication Losses

Despite the progresses in Cooperative Adaptive Cruise Control (CACC), a crucial limitation of the state-of-the-art of this control scheme is that the string stability of the platoon can be proven only when the vehicles in the platoon have identical driveline dynamics (homogeneous platoons). In this paper, we present a novel control strategy that overcomes the homogeneity assumption and that is able to adapt its action and achieve string stability even with uncertain heterogeneous platoons with unknown engine performance losses and inevitable communication losses. Considering a one-vehicle look-ahead topology, we propose an adaptive switched control strategy: the control objective is to switch from an augmented CACC to an augmented Adaptive Cruise Control strategy when communication is lost based on a dwell time characterized switching law. The simulation of the proposed control strategy is conducted to validate the theoretical analysis.

Adaptive fuzzy fault‐tolerant control for multiple high‐speed trains with proportional and integral‐based sliding mode

In this study, novel adaptive fuzzy fault-tolerant control method is proposed for multiple high-speed trains (HSTs) in the presence of actuator faults, unknown non-linear dynamics and external disturbances. The fuzzy logic system is used to approximate the unknown functions. Based on proportional and integral-based sliding mode technique, two adaptive fuzzy control schemes are then proposed to achieve string stability. In the first scheme, the actuator faults are not considered. In the second scheme, a novel fuzzy fault-tolerant control with fewer adjustable parameters is constructed to further reduce the online computational load. By using Lyapunov analysis, the individual stability and string stability of whole multiple HSTs are proven. In addition, all signals of the closed-loop system are uniformly ultimately bounded and all HSTs track the reference trajectory to a small compact set around zero. Finally, comparative simulation is introduced to verify the reliability and effectiveness.

Leader tracking in homogeneous vehicle platoons with broadcast delays

For vehicle platoons, the leader following control architecture is known to be capable of achieving string stability while maintaining tight formations. In this paper, we study a variety of schemes where the leader state is available to the other members of the platoon. We show that in some cases it is possible to achieve string stability in the presence of certain amounts of time delay in the leader state reception. We also compare other properties of the different schemes and discuss some of their advantages and disadvantages.