## 3 LB-MPC in Path Tracking of Mobile Platforms
### Learning and Optimizing for Controller
#### 3.2.1 Learning and Optimizing for Control Precision  
The model predictive controller optimizes the cost function under various constraints. The optimization design of the controller precision is based on the parameterization of the cost function and constraints. The cost function and the constraint condition can be parameterized into the function of the system state variables, application input, and random variables. Table 3 shows a parameterized version of an MPC problem, including a parameterization of the cost function \(l(x_{i},u_{i},\theta_{t})\) and constraints \(\mathcal{X}(\theta_{\mathcal{X}})\), \(\mathcal{U}(\theta_{\mathcal{U}})\)[31]. This is convenient for subsequent learning and optimization of the controller parameters under uncertain disturbances. Figure 6: The path randomization for training [97]. It is difficult to track the paths effectively by using the model-based controller under uncertain environments. In addition, it is unrealistic to adjust the controller parameters manually for all the conditions. In order for the aforementioned problems to be solved, the data-driven ML methods described in Section 3.1 are usually used to estimate the environmental disturbance, and the data-driven model is used to design the controller. However, the lack of data can easily lead to incorrect approximation of uncertain disturbances. Therefore, the adaptive predictive control strategy is the key to achieving high-performance path tracking control. The recorded data are converted to the corresponding MPC parameters. On one hand, the closed-loop performance is improved by adjusting the parameterized cost function and constraint conditions on the basis of the performance-driven controller learning. On the other hand, the path tracking controller adjusts its parameters online by adapting to uncertain environmental disturbances. The input and state trajectories of the dynamic system are parameterized by the basis function to reduce the computational complexity of MPC [98]. When the input constraints are considered, the uncertainty is estimated and compensated in the design of the controller, and the recorded data are converted to the corresponding parameterization of the MPC problem. The performance-driven controller learning focuses on finding the parameterization of the cost function and constraint conditions in MPC. The closed-loop performance is optimized by solving the optimal control problem. One solution is to adjust the controller on the basis of Bayesian optimization, and the other solution is to learn the terminal components to counteract the finite-horizon nature of the controller. The Bayesian optimization method models the unknown function as a GP, evaluates the function, and guides it to the optimal position. Then, the controller parameters are estimated on the basis of experiments to optimize the controller performance. The information samples in Bayesian optimization are usually far away from the original control law, which leads to unstable evaluation and system failure of the controller in the early optimization process [99]. The security problems are solved by using the improved security optimization controllers and exploring new controller parameters whose performance lies above a safe performance threshold [100]. By combining the linear optimal control with Bayesian optimization, a parameterized cost function is introduced and optimized to