论文标题
汉密尔顿 - 雅各比 - 贝尔曼方程的数据驱动张量火车梯度交叉近似
Data-driven Tensor Train Gradient Cross Approximation for Hamilton-Jacobi-Bellman Equations
论文作者
论文摘要
提出了一种梯度增强的功能张量列车交叉近似方法，用于介绍与非线性动力学最佳反馈控制相关的汉密尔顿 - 雅各比 - 贝尔曼（HJB）方程。该过程使用HJB方程及其梯度的溶液的样品来获得值函数的张量列近似。该算法的数据收集基于两种可能的技术：Pontryagin最大原理和状态依赖性Riccati方程。几个数值测试以低维度和高维表示，显示了所提出的方法的有效性及其相对于梯度信息提供的不精确数据评估的鲁棒性。所得的张量训练近似为实时应用中的控制信号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 to 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.
