A data-driven approximate solution to the model-free HJB equation

作者：Huang, Zhijian^*; Li, Yudong; Zhang, Cheng; Wu, Gang; Liu, Yihua; Chen, Yuli

来源：Optimal Control Applications and Methods, 2018, 39(2): 835-844.

DOI：10.1002/oca.2381

• data-driven
• Hamilton function
• Hamilton-Jacobi-Bellman
• online
• optimal
• tracking differentiator

It is generally impossible to analytically solve the Hamilton-Jacobi-Bellman (HJB) equation of an optimal control system. With the coming of the big-data era, this paper first derives a new data-driven and model-free Hamilton function for the HJB equation. Then, a data-driven tracking differentiator method is proposed to solve the Hamilton function. Finally, the simulation for a classic example shows that the optimal control policy can be approximated with the proposed method. Thus, an online data-driven model-free approximate solution to the HJB equation is achieved. This method is only driven by the measured system states. All other variables and derivatives can be derived from the data-driven model-free Hamilton function and tracking differentiator. The method has a complete mathematical support and works like a controller. It does not need neural networks and has no training or iterative convergence problem. Thus, this paper adds an online data-driven model-free method to the existing literature on the approximate solution to the HJB equation.

• 出版日期2018-4
• 单位上海海事大学