Model-free output feedback optimal tracking control for two-dimensional batch processes

To address the challenge of linear quadratic tracking for batch processes without taking into account the specifics regarding the system dynamics and the state observer, a two-dimensional off-policy model-free output feedback control method is proposed. Previous solutions have mostly failed to fully explore the historical input and output information of the system along time and batch dimensions, thereby constraining the flexibility and efficiency of the controller. However, the method proposed aims to reconstruct the state space by delving into these historical input and output data of the system. The correlation between the two-dimensional value function and the twodimensional Q-function with output feedback characteristics is found, thereby revealing the corresponding twodimensional Bellman equation. This method, through the use of reinforcement learning algorithms, can effectively learn the optimal control strategy without the need for prior knowledge of system dynamics. To this end, the proposed method not only converges faster but also has smaller errors, making it more suitable for complex and ever-changing industrial production processes in reality. This innovative research provides new ideas and methods for the design and optimization of control systems, which is expected to bring higher efficiency and more stable performance to industrial production. At last, simulation outcomes for the injection velocity process validate the suggested method's effectiveness.