## 1 Introduction  
With the growing demand for transportation in modern society, concern about road safety and traffic congestion is increasing [1; 2]. Intelligent transportation systems are regarded as a promising solution to these challenges due to their potential to significantly increase road capacity, enhance safety, and reduce fuel consumption [3; 4]. As a representative application for intelligent transportation, adaptive cruise control (ACC) systems have been extensively studied by academia and industry and are commercially available in a wide range of passenger vehicles. ACC utilizes a range sensor (camera and/or radar) to measure the inter-vehicle range, and the relative velocity and controls the longitudinal motion of the host vehicle to maintain a safe distance from the preceding vehicle [5]. As a result, the driver is free from frequent acceleration and deceleration operation, and driving comfort and safety are improved. In recent years, the development of vehicle-to-vehicle (V2V) communication technologies, such as DSRC and LTE-V [6, 7], has provided an opportunity for the host vehicle to exchange information with its surrounding vehicles. The resulting functionality, named cooperative adaptive cruise control (CACC), utilizes information on the forward vehicle or vehicles via V2V, as well as the inter-vehicle distance and relative velocity. Compared with conventional ACC, the wireless communication devices for CACC system increase cost of on-board hardwares. The control strategy becomes more complicated due to additional system state variables and the topological variety for platoons, which are even more critical when considering time delay, packet loss, and quantization error in the communications [8, 9]. In [10], it is demonstrated that the string stability domains shrink when the packet drop ratio or the sampling time of communication increases and above a critical limit string stability cannot be achieved. In [11], an optimal control strategy is employed to develop a synthesis strategy for both distributed controllers and the communication topology that guarantees string stability. In another hand, CACC is more attractive than conventional autonomous ACC, because the system behavior is more responsive to changes in the preceding vehicle speed, thereby enabling shorter following gaps and enhancing traffic throughput, fuel economy, and road safety [12]. Simulation results revealed that the freeway capacity increases quadratically as the CACC market penetration increases, with a maximum value of 3080 veh/h/lane at 100% market penetration, which is roughly 63% higher than at 0% market penetration [13, 14]. The earliest research on CACC dates to the PATH program [15] in the US, which was followed by the SARTRE project [16, 17] in Europe and the Energy ITS project [18] in Japan. Another demonstration of CACC is the Grand Cooperative Driving Challenge (GCDC), which has been held twice in 2011 and 2016 in the Netherlands. In GCDC, several vehicles cooperated in both urban and highway driving scenarios to facilitate the deployment and research of cooperative driving systems based on a combination of communication and state-of-the-art sensor fusion and control [19, 20]. Most research on CACC has focused on vehicle dynamics control in the longitudinal direction to achieve stable following and coordination of the platoon. Linear feedforward and feedback controllers are widely used due to their advantages of simple structure and convenience in hardware implementation [21, 22, 23]. In this approach, the controller uses the acceleration of the preceding vehicle and tracking errors as the feedforward and feedback signals, respectively, to determine the desired acceleration of the host vehicle. However, due to the nonlinearity of vehicle dynamics and uncertainty of the environment, sets of controller parameters need to be tuned manually, and it is difficult for controllers to be adaptive and robust to unknown disturbances.