Tensor Decomposition Methods for High-dimensional Hamilton--Jacobi--Bellman Equations
Tensor Decomposition Methods for High-dimensional Hamilton--Jacobi--Bellman Equations
复制标题
高维Hamilton--Jacobi--Bellman方程的张量分解方法
DOI：
10.1137/19m1305136
复制
发表时间：
2021
影响因子：
3.1
通讯作者：
Dolgov S
中科院分区：
文献类型：
--
作者：
Dolgov S
本文提出了一种张量分解方法，用于求解非线性动力学最优反馈控制中的高维、完全非线性汉密尔顿-Jacobi-Bellman方程。该方法结合了张量列车近似值函数与牛顿迭代法的解决方案所产生的非线性系统。张量近似导致关于维度的多项式缩放，部分地规避了维度灾难。线性二次的情况下的收敛性分析。对于非线性动力学，本文用高维控制综合方法对100个变量的艾伦-卡恩和福克-普朗克方程的最优反馈镇定问题进行了研究.
A tensor decomposition approach for the solution of high-dimensional, fully nonlinear Hamilton--Jacobi--Bellman equations arising in optimal feedback control of nonlinear dynamics is presented. The method combines a tensor train approximation for the value function together with a Newton-like iterative method for the solution of the resulting nonlinear system. The tensor approximation leads to a polynomial scaling with respect to the dimension, partially circumventing the curse of dimensionality. A convergence analysis for the linear-quadratic case is presented. For nonlinear dynamics, the effectiveness of the high-dimensional control synthesis method is assessed in the optimal feedback stabilization of the Allen--Cahn and Fokker--Planck equations with a hundred of variables.