Data-Driven Tensor Train Gradient Cross Approximation for Hamilton-Jacobi-Bellman Equations
Data-Driven Tensor Train Gradient Cross Approximation for Hamilton-Jacobi-Bellman Equations
复制标题
Hamilton-Jacobi-Bellman 方程的数据驱动张量训练梯度交叉逼近
DOI：
10.1137/22m1498401
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发表时间：
2023
影响因子：
3.1
通讯作者：
Dolgov S
中科院分区：
文献类型：
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作者：
Dolgov S
提出了一种求解非线性动力学最优反馈控制的Hamilton-Jacobi-Bellman（HJB）方程的梯度增强泛函张量列交叉逼近方法.该程序使用HJB方程的解及其梯度的样本来获得值函数的张量序列近似。该算法的数据收集是基于两种可能的技术：庞特里亚金最大值原理和状态依赖的Riccati方程。几个数值试验中提出的低，高的维度显示所提出的方法的有效性和其鲁棒性相对于不精确的数据评估，所提供的梯度信息。由此产生的张量序列近似为实时应用中控制信号的快速合成铺平了道路。
A gradient-enhanced functional tensor train cross approximation method for the resolution of the Hamilton–Jacobi–Bellman (HJB) equations associated with optimal feedback control of nonlinear dynamics is presented. The procedure uses samples of both the solution of the HJB equation and its gradient to obtain a tensor train approximation of the value function. The collection of the data for the algorithm is based on two possible techniques: Pontryagin Maximum Principle and State-Dependent Riccati Equations. Several numerical tests are presented in low and high dimension showing the effectiveness of the proposed method and its robustness with respect to inexact data evaluations, provided by the gradient information. The resulting tensor train approximation paves the way towards fast synthesis of the control signal in real-time applications.