# Adaptive Cruise Control for Cut-In Scenarios Based on Model Predictive Control Algorithm
## 1 Introduction  
With the rapid development of computers, electronics, and sensor technology, advanced driver assistance systems (ADAS) have now become an important direction for development of the automotive industry because they have great advantages in improving transportation efficiency [1] and driving safety [2]. As an important branch of ADAS, ACC systems have a wide range of applications in car-following scenarios. However, complex driving scenarios, such as cut-in scenarios, are still challenging for ACC systems [3]. When facing the lane-change maneuvers of a nearby car, a vehicle with an ACC system has to switch the following target to the cut-in vehicle and follow its trajectory. In this process, there may be a problem of braking too late as well as excessive braking. In order to ensure driving safety and driving comfort, the cut-in possibility of a nearby car needs to be determined. When facing a vehicle cut-in, the host vehicle with the ACC system needs to cooperate with the cut-in vehicle at the same time, and smoothly follow the cut-in vehicle. In ACC control, the aim is to solve the optimal control law of the host vehicle under the condition of satisfying constraints. Therefore, ACC can be considered as a constrained optimization problem. For constrained optimization methods, [PERSON] et al. [4] and [PERSON] et al. [5] proposed a novel scheme called the explicit reference governor (ERG) for the control of constrained systems characterized by fast dynamics and that are subject to non-convex constraints. [PERSON] et al. [6] proposed a systematic approach for applying the ERG to linear systems subject to combinations of intersections and unions of concave constraints. In addition, [PERSON] et al. [7] first utilized the barrier functions in constrained optimization. In constrained optimization, a barrier function is a continuousfunction in which the value of a point increases to infinity as the point approaches the boundary of the feasible region; therefore, a barrier function is used as a penalizing term for violations of constraints [8]. However, in the process of following a preceding vehicle, the motion state of the preceding vehicle changes dynamically, so the control method of the host vehicle needs to be continuously adjusted. Model predictive control (MPC) can divide the time domain into infinite finite horizons. In each horizon, which is a sample time, the system experiences an error with the reference trajectory. With this error minimization as the control objective, the optimal control law is solved under constraints, and then the control law is used as the input of the system at the next horizon until the system reaches the reference trajectory. This is considered a rolling optimization process. Therefore, MPC is more suitable for the following control of a host vehicle. In addition, MPC can take the acceleration of the preceding vehicle as a disturbance in the system control, which compensates for the uncertainty caused by the preceding vehicle. For instance, [PERSON] et al. [9] proposed an MPC-based headway control algorithm, which explicitly incorporates acceleration limits to meet the requirements of ride comfort and safety. Except for MPC, many studies have contributed to the ACC control method. [PERSON] et al. [10] proposed the design, development, implementation, and testing of a cooperative adaptive cruise control system. [PERSON] et al. [11] analyzed an ACC system using the method of transition state variables and obtained a desired acceleration. [PERSON] et al. [12] studied the motion characteristics of an adaptive cruise system using a non-linear method with finite time constraints. [PERSON] et al. [13] optimized the non-linear characteristics of a vehicle into linear characteristics, thereby using the linear time-invariant model to control the ACC tracking index. [PERSON] et al. [14] conducted real-time research and observations on a vehicle dynamic model, and optimized the adaptive cruise system algorithm by using the minimum tracking method. [PERSON] et al.