Lei Ding,, Jie Li, Maojiao Ye,,and Yuan Zhao

Dear Editor,

This letter is concerned with distributed resilient platoon control of multiple vehicles subject to denial-of-service (DoS) attacks. In order to accommodate the effects of DoS attacks, a fully resilient distributed control strategy is presented by designing an adaptive control gain, where any global information of communication topology is no longer required. Then, the conditions of time duration rates and frequency of DoS attacks on stability of vehicular platoons can be characterized. Finally, a numerical simulation example is given to validate the obtained results.

Coordinated platoon control, which aims to drive vehicles to follow each other at a specific predefined distance, is an important technical means in transportation systems to improve traffic safety,alleviate traffic congestion, and improve traffic pollution [1]. In order to achieve such coordinated platoon control, various distributed algorithms have been developed for vehicular platoon systems[2]–[6]. For example, a sampled-data-based cooperative scheme is proposed to achieve platoon control [2]. Based on multi-agent consensus protocols, a decomposition framework was introduced to model, analyze and design platoon systems [3]. An adaptive sliding mode control protocol was developed in [4], where the communication interactions among the vehicles were considered to be uncertain. An optimized control method was proposed for distributed cooperative vehicular platoon systems by considering actuator delays and non-ideal communication conditions [5]. A platooning control scheme with dynamic event-triggered scheduling is presented [6]. However, it should be pointed out that most of existing distributed vehicular platoon control schemes require some Laplacian eigenvalue information associated with the communication graph. In practical situations, it is difficult, costly or even impossible to calculate such global information for each vehicle. Thus, it is desirable for vehicle platoon systems to design a fully distributed control scheme without requiring any knowledge of global information. To address this issue, a fully distributed control strategy was developed for vehicular platoon systems based on an eventtriggered communication scenario [7].

Note that communication topologies for distributed control systems are often vulnerable to cyber attacks controlled by malicious actions or accidents [8], [9]. DoS attacks, as one of the most common types of attacks, often cause the paralysis of communication connectivity by blocking the data transmission through communication channels,probably leading to undesirable consequences, such as performance degradation or even head-to-tail collisions [10]. To relax the negative effects caused by DoS attacks, a variety of secure control schemes have been investigated. For example, some network recovery mechanisms was introduced to recover vehicle-to-vehicle (V2V)communication networks damaged by DoS attacks [11]. Moreover, a linear matrix inequality (LMI)-based controller adjustment program was provided in [12]. Based on adaptive and sliding mode control,observer-based approaches were designed to accommodate DoS attacks [13]. Distributed secure control for connected vehicles under DoS attacks was considered [14], [15]. However, such distributed control algorithms [14], [15] are not fully distributed, as the global information of communication topologies is required. Therefore, it is interesting yet challenging to develop a fully distributed resilient control scheme for vehicle systems subject to DoS attacks, which motivates the current study.

Motivated by the above observation, this letter aims to develop fully distributed secure platoon control strategies for multiple vehicle systems subject to DoS attacks. The main contributions of this letter can be summarized as: 1) Different from [14], [15], a fully resilient distributed control scheme under DoS attacks is developed in the letter. By designing adaptive protocols for the control gains, the method does not require any global information. 2) A sufficient condition is derived to ensure the stability of vehicle platoon, where the effects of duration time and frequency of DoS attacks on stability of vehicle platoon can be revealed.

Fig. 1. Switching communication topologies caused by DoS attacks.

Fig. 2. Switching mapping σ (t) of communication topology.

With the provided parameters, the followers’ position trajectories,velocity and spacing error trajectories are depicted in Figs. 3?5,respectively. It is shown in Fig. 3 that each follower vehicle can achieve the leader tracking during the whole simulation. From Figs. 4 and 5, it is demonstrated that all follower vehicles is capable of tracking the leader’s velocity while maintaining a desired distance from its front and behind vehicles, although their velocities and distance errors suffer from a large deviation under cyber attacks. Fig. 6 shows vehicles’ accelerations, from which it is clear that they are convergent to zero. Fig. 7 depicts the adaptive gain values of six followers. It can be seen that the adaptive gain values converge to some finite values. Hence, the proposed control design has been numerically verified.

Fig. 3. Vehicles’ positions under DoS attacks.

Fig. 4. Vehicles’ velocities under DoS attacks.

Fig. 5. Vehicles’ spacing errors under DoS attacks.

Fig. 6. Vehicles’ accelerations under DoS attacks.

cri(t)Fig. 7. Adaptive gains of vehicles under DoS attacks.

Conclusions: In this letter, vehicular platoon control under DoS attacks has been investigated. A fully distributed control scheme has been presented for ensuring the stability of vehicular platoon systems. By adaptively adjusting the parameter of the control scheme, global information does not need to be calculated. Then, a sufficient condition has been derived to achieve the controller gain design. In the future, co-existence of multiple cyber attacks and communication channels with limited capacities will be considered.

Acknowledgments: This work was supported by the National Natural Science Foundation of China (NSFC) (62073171, 62173181),the Natural Science Foundation of Jiangsu Province (BK20200744,BK20180455), Jiangsu Specially-Appointed Professor (RK043 STP19001), 1311 Talent Plan of Nanjing University of Posts and Telecommunications, the Fundamental Research Funds for the Central Universities (30920032203), the Natural Science Foundation of Tianjin (20JCQNJC00390), and Graduate Scientific Research Innovation Project of Tianjin (2021YJSO2S31).