## 1 Introduction
### Literature Review  
The design of trajectory tracking controllers based on the classical control theory is undoubtedly one of the efficient and feasible methods to quickly realise the single target tracking problem. In the autonomous vehicle off-road challenge organised by the U.S. Defense Advanced Research Projects Agency (DARPA) in 2005, [PERSON] of Stanford University successfully won the championship [3], and its lateral tracking controller was designed based on the classical PID control theory, which further verified the feasibility of using the classical PID control to achieve single target tracking. In addition, Nissan [4] designed a feedforward-feedback controller using the classical PID method to realise the tracking control of autonomous vehicle trajectory under continuous speed change and solved the real-time problem of longitudinal and lateral control of the autonomous vehicle. Aiming at the path tracking problem under significant curvature path conditions, a state feedback PID control strategy based on the optimal path was proposed to enhance the robustness of the lateral control system to the change of path curvature [5]. [PERSON] et al. [6] considered the enormous energy consumption of the suspension robot in the path tracking and optimised the control parameters of the traditional PID controller using the genetic algorithm. Through the online parameter adjustment, the energy consumption of the suspension robot could be significantly reduced when the designed PID controller tracks the same trajectory. In addition, researchers have also expanded other control algorithms for single target trajectory tracking. [PERSON] and [PERSON] [7] designed the coordinated control algorithm of longitudinal and lateral control based on the robust adaptive control theory and compared the traditional coordinated control algorithm with the longitudinal and lateral decoupling control algorithm. The results showed the superiority of longitudinal and lateral coordinated control of the autonomous vehicle. [PERSON] et al. [8], based on the analysis of the maximum cornering force of the tire and the steady-state characteristics of the vehicle, proposed the planning control method of the slip envelope to continuously approach the driving speed limit of the autonomous vehicle on the premise of preventing the vehicle from slipping. [PERSON] et al. [9] constructed the RBF neural network adaptive longitudinal and lateral coordinated control strategy and analysed the stability of the control system through Lyapunov theory, which could ensure the uniform convergence and boundedness of tracking error. [PERSON] et al. [10] proposed a control method based on the expected azimuth deviation estimator and robust PID feedback controller for trajectory tracking control under variable speed conditions and verified that the vehicle had a good trajectory tracking performance under different speed conditions. [PERSON] et al. [11] proposed an H \(\infty\) robust static output feedback control method combining genetic algorithm and linear matrix inequality method to study the tracking problem of an autonomous vehicle. The proposed controller was robust to external disturbances and vehicle/environmental parameter/state uncertainties, including the tire cornering stiffness, the longitudinal vehicle speed, the yaw rate and the road curvature. Constraint processing and multi-target tracking are inevitable in the trajectory tracking control of the autonomous vehicle in practice, and the extended classical PID control cannot deal with time-varying constraints and multi-target tracking. At present, for the problem of multi constraint processing and multi-target tracking in autonomous vehicle tracking control, model predictive control (MPC) based on optimal control theory is undoubtedly one of the most widely studied and applied control algorithms. In this regard, [PERSON] et al. [12] proposed longitudinal and lateral control strategies based on MPC and realised the expected speed and expected path following. [PERSON] et al.