Data-driven Tensor Train Gradient Cross Approximation for Hamilton-Jacobi-Bellman Equations

2022/05/10 by Sergey Dolgov, Dolgov, Sergey, Dante Kalise +3 · 2 citations
Mathematics · #15A23 #15A69 #49J20 #49LXX #49MXX #65F10 #65N22 #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2205.05109

openalex publication_date 2022/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Implicit Tensor-Train Cross Integration of High-Dimensional Nonlinear PDEs via Fiber-Dependency Elimination
• High order Tensor-Train-Based Schemes for High-Dimensional Mean Field Games

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