## 1 Introduction  
A variety of issues, such as traffic jams, traffic collisions, and air pollution, are becoming more and more serious in modern transport systems [1, 2, 3, 4, 5]. Vehicle platoon control refers to coordinating and regulating the movement of a group of vehicles in a transportation network to guarantee that the transport system operates efficiently and safely [6]. Vehicle platoon control has shown significant advantages in increasing the traffic volume of roads, reducing traffic congestion, and improving the efficiency of traveling [7, 8, 9]. To address traffic problems, the field of vehicle platoon control has attracted growing attention [10, 11]. Fundamental issues in the vehicle platoon field which have been studied include homogeneous or heterogeneous dynamics [12], stability analysis [13], spacing policies [14], and others. Maintaining consistent spacing between adjacent vehicles and achieving velocity synchronization of followers with the leader are the primary control goals of use of a platoon [15]. Issues such as the degradation of control performance and instability of a vehicle platoon in practice are usually caused by unknown external disturbances [16; 17]. Disturbances that appear in the control input channel are usually classified as matched disturbances, such as those involving model uncertainty, rolling resistance, and gusts of wind [18]. Disturbances which do not appear in the control input channel are usually classified as mismatched disturbances, such as unmodeled dynamics, dynamic friction, and velocity uncertainty [19]. Numerous studies have been carried out to reduce the impact of unknown external disturbances on vehicle platoons [20; 21; 22; 23]. In [20], the article considers the robust control problem confronted by a vehicle platoon when subjected to matched disturbances, and presents a distributed \(H_{\infty}\) control strategy designed to effectively accomplish the control goals of the platoon. Ref. [21] integrates a disturbance observer and a multi-power convergence method into a coupled sliding mode controller, aiming to counteract the adverse effects induced by matched disturbances. An investigation of platoon control issues, particularly those arising from matched disturbances, is presented in [22], which proposes a distributed adaptive sliding mode control approach to effectively handle disturbances and ensure that a vehicle platoon achieves the predetermined tracking performance. The authors of [23] present an adaptive event-triggered control strategy that can effectively deal with matched disturbances and synchronize a vehicle platoon. It is to be noted that only the matched disturbances of a vehicle platoon are considered in the control methods mentioned above. However, in practice, mismatched disturbances may also degrade control performance and even cause instability of the platoon control system [19]. In recent studies, several control schemes have been presented for systems under mismatched disturbances to solve the issues caused by such disturbances [24; 25]. In [25], a nonsingular dynamic terminal sliding mode control method is developed, where both matched and mismatched disturbances are effectively compensated, thereby guaranteeing the stability of the vehicle platoon under intermittent communication conditions. Ref. [26] develops a disturbance observer-based nonsingular terminal sliding mode control scheme to effectively mitigate both matched and mismatched disturbances of a vehicle platoon, ensuring system stability while optimizing platoon control performance. Ref. [27] investigates a distributed adaptive singularity-free fixed-time neural network tracking control problem for a vehicle platoon with mismatched disturbance, where a novel backstepping control architecture synergistically integrating a neural network is developed to effectively address mismatched disturbance. It is to be noted that nearly all the aforementioned works assume that the precise upper bounds of mismatched disturbances are known.