Data-driven initialization of deep learning solvers for Hamilton-Jacobi-Bellman PDEs

A deep learning approach for the approximation of the Hamilton-Jacobi-Bellman partial differential equation (HJB PDE) associated to the Nonlinear Quadratic Regulator (NLQR) problem. A state-dependent Riccati equation control law is first used to generate a gradient-augmented synthetic dataset for su...

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Bibliographic Details
Published in:arXiv.org 2022-07
Main Authors: Borovykh, Anastasia, Kalise, Dante, Laignelet, Alexis, Parpas, Panos
Format: Article
Language:English
Subjects:
Deep learning
Optimization
Partial differential equations
Riccati equation
Online Access:Get full text
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Summary:A deep learning approach for the approximation of the Hamilton-Jacobi-Bellman partial differential equation (HJB PDE) associated to the Nonlinear Quadratic Regulator (NLQR) problem. A state-dependent Riccati equation control law is first used to generate a gradient-augmented synthetic dataset for supervised learning. The resulting model becomes a warm start for the minimization of a loss function based on the residual of the HJB PDE. The combination of supervised learning and residual minimization avoids spurious solutions and mitigate the data inefficiency of a supervised learning-only approach. Numerical tests validate the different advantages of the proposed methodology.
ISSN:2331-8422