## 2 Overview of Learning-Based Model Predictive Control  
### Model Predictive Control  
Currently, the MPC is a well-known and standard technique used for implementing constrained and multivariable control in process industries [33; 34]. It provides an integrated solution for path tracking control in mobile platforms [35; 36; 37]. Unlike other optimal control methods, MPC employs a unique receding horizon technique that enables rescheduling of the optimal control strategies at each control interval to eliminate the accumulation of control errors. In mobile platforms, the MPC first establishes a prediction model. Then, all the possible states of the mobile platforms are predicted by combining the current state of the mobile platforms and the feasible control input. Finally, the state closest to the reference  
Figure 1: The development process of LB-MPC [4; 5; 6; 7; 8; 9; 32].  
state is obtained by optimizing the cost function, and the corresponding control input is attained. The MPC aims to achieve optimality in a long period of time on the basis of short-term optimization. This process involves three major steps, namely, prediction using model, rolling optimization, and feedback correction. The combination of prediction and optimization is the main difference between MPC and other control methods.  
However, the MPC needs to consider the perception and response to the time-varying characteristics of a system that are caused by the uncertain disturbances. The dynamic characteristics of a system increase the uncertainty, thus affecting the performance of MPC [38; 39]. In practice, model descriptions can be subject to considerable uncertainty, originating, e.g., from insufficient data, restrictive model classes, or the presence of external disturbances. Therefore, it is necessary to actively learn the uncertainties in a system and incorporate regular adaption for preserving the performance of MPC in uncertain systems.  
The MPC for path tracking control in mobile platforms can be divided into linear model predictive control (LMPC), linear error model predictive control (LEMPC), nonlinear model predictive control (NMPC), and nonlinear error model predictive control (NEMPC). Figure 2 presents the comparisons of the articulated vehicle path tracking controller on the basis of LMPC, LEMPC, NMPC, and NEMPC when tracking the path with complex curvature variation [40]. The simulation results show that the performance of the NMPC controller is better as compared to LMPC, LEMPC, and NEMPC controllers. The articulated vehicle path tracking controller based on NMPC performs well in terms of stability and accuracy. However, NMPC controller needs to be further optimized in real time. Therefore, the NMPC controllers are usually used for path tracking of robots [41]. Additionally, the whole algorithm efficiency can be improved by the prediction model, cost function, and minimization algorithm.  
The MPC has the ability to deal with general nonlinear dynamics, hard state, input constraints, and general cost functions. Currently, solving online optimization problems has become a future research trend of MPC due to its high computational complexity.  
Figure 2: Comparisons of LMPC, LEMPC, NMPC, and NEMPC [40].  
Especially in the cases of complex physical models, numerous optimization variables, or high sampling frequency, the online optimization becomes more difficult. Moreover, it is noteworthy that the MPC is usually set up in advance by the controller and is difficult adjust in accordance with the situation. The availability of increasing computational power and sensing and communication capabilities, as well as advances in the field of machine learning, has given rise to a renewed interest in automating controller design and adaptations based on data collected during operation, e.g., for improved performance, facilitated deployment, and a reduced need for manual controller tuning.