A Data-driven Approximate Solution to the Model-free HJB Equation
A Data-driven Approximate Solution to the Model-free HJB Equation
复制标题
无模型HJB方程的数据驱动近似解
DOI：
10.1002/oca.2381
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Chen Yuli
中科院分区：
文献类型：
--
作者：
Huang Zhijian;Li Yudong;Zhang Cheng;Wu Gang;Liu Yihua;Chen Yuli
通常不可能解析求解最优控制系统的 Hamilton-Jacobi-Bellman (HJB) 方程。随着大数据时代的到来，本文首先针对HJB方程推导了一种新的数据驱动、无模型的Hamilton函数。然后，提出了一种数据驱动的跟踪微分器方法来求解汉密尔顿函数。最后，通过经典算例的仿真表明，该方法可以逼近最优控制策略。由此，实现了 HJB 方程的在线数据驱动无模型近似解。该方法仅由测量的系统状态驱动。所有其他变量和导数都可以从数据驱动的无模型汉密尔顿函数和跟踪微分器中导出。该方法具有完整的数学支持，并且像控制器一样工作。它不需要神经网络，也不存在训练或迭代收敛问题。因此，本文在现有关于HJB方程近似解的文献中添加了一种在线数据驱动的无模型方法。
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 completemathematical support andworks 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.