Implementation of Optimal Control Method

This example utilizes optimal control theory with quadratic performance indices to ensure optimal performance in both the cart's sliding distance and energy consumption throughout the operation. Specifically, we first establish the dynamic model of the cart and select appropriate control strategies, such as PID controllers. Then, we apply methods from optimal control theory, including Pontryagin's minimum principle, to compute the optimal controller. Finally, we validate the controller's performance through simulation experiments. The program consists of the following files: - initial.m: Initialization script that sets up system parameters, initial conditions, and simulation environment configuration - yjlqgctr.m: Controller design program implementing LQG (Linear Quadratic Gaussian) control algorithms with quadratic cost function optimization - cartoon.m: Visualization module that generates animated plots and real-time performance graphs of the cart's motion - simlqgyj.slk: Simulink model file containing the complete simulation framework for testing and validating the control system performance