A Physics-Informed Learning Framework to Solve the Infinite-Horizon Optimal Control Problem

• URL: http://arxiv.org/abs/2505.21842v1
• Date: Wed, 28 May 2025 00:21:49 GMT
• Title: A Physics-Informed Learning Framework to Solve the Infinite-Horizon Optimal Control Problem
• Authors: Filippos Fotiadis, Kyriakos G. Vamvoudakis,
• Abstract summary: We propose a physics-informed neural networks (PINNs) framework to solve the infinite-horizon optimal control problem of nonlinear systems.<n>We tackle this by instead applying PINNs to a finite-horizon variant of the steady-state HJB that has a unique solution.<n>Unlike many existing methods, the proposed technique works well with non-polynomial basis functions.
• Score: 4.2402873718254535
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a physics-informed neural networks (PINNs) framework to solve the infinite-horizon optimal control problem of nonlinear systems. In particular, since PINNs are generally able to solve a class of partial differential equations (PDEs), they can be employed to learn the value function of the infinite-horizon optimal control problem via solving the associated steady-state Hamilton-Jacobi-Bellman (HJB) equation. However, an issue here is that the steady-state HJB equation generally yields multiple solutions; hence if PINNs are directly employed to it, they may end up approximating a solution that is different from the optimal value function of the problem. We tackle this by instead applying PINNs to a finite-horizon variant of the steady-state HJB that has a unique solution, and which uniformly approximates the optimal value function as the horizon increases. An algorithm to verify if the chosen horizon is large enough is also given, as well as a method to extend it -- with reduced computations and robustness to approximation errors -- in case it is not. Unlike many existing methods, the proposed technique works well with non-polynomial basis functions, does not require prior knowledge of a stabilizing controller, and does not perform iterative policy evaluations. Simulations are performed, which verify and clarify theoretical findings.

Related papers

• Solving nonconvex Hamilton--Jacobi--Isaacs equations with PINN-based policy iteration [1.3654846342364308]
  We present a framework that combines classical dynamic programming with neural networks (PINNs) to solve non-subscriber Hamilton-Jacobi-Isaac equations.<n>Our results suggest that integrating PINNs with policy policy is a practical and theoretically grounded method for solving high-dimensional, nonsubscriber HJI equations.
  arXiv  Detail & Related papers  (2025-07-21T10:06:53Z)
• Neural Actor-Critic Methods for Hamilton-Jacobi-Bellman PDEs: Asymptotic Analysis and Numerical Studies [3.566534591413616]
  We mathematically analyze and numerically analyze an actor-critic machine learning algorithm for solving HamiltonJacobiBellman equations.<n>In our numerical studies, we demonstrate that the algorithm can solve control problems accurately in up to 200 dimensions.
  arXiv  Detail & Related papers  (2025-07-08T22:20:22Z)
• Hamilton-Jacobi Based Policy-Iteration via Deep Operator Learning [9.950128864603599]
  We incorporate DeepONet with a recently developed policy scheme to numerically solve optimal control problems. A notable feature of our approach is that once the neural network is trained, the solution to the optimal control problem and HJB equations can be inferred quickly.
  arXiv  Detail & Related papers  (2024-06-16T12:53:17Z)
• Operator Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations Characterized by Sharp Solutions [10.999971808508437]
  We propose a novel framework termed Operator Learning Enhanced Physics-informed Neural Networks (OL-PINN) The proposed method requires only a small number of residual points to achieve a strong generalization capability. It substantially enhances accuracy, while also ensuring a robust training process.
  arXiv  Detail & Related papers  (2023-10-30T14:47:55Z)
• Constrained Optimization via Exact Augmented Lagrangian and Randomized Iterative Sketching [55.28394191394675]
  We develop an adaptive inexact Newton method for equality-constrained nonlinear, nonIBS optimization problems. We demonstrate the superior performance of our method on benchmark nonlinear problems, constrained logistic regression with data from LVM, and a PDE-constrained problem.
  arXiv  Detail & Related papers  (2023-05-28T06:33:37Z)
• Stochastic Inexact Augmented Lagrangian Method for Nonconvex Expectation Constrained Optimization [88.0031283949404]
  Many real-world problems have complicated non functional constraints and use a large number of data points. Our proposed method outperforms an existing method with the previously best-known result.
  arXiv  Detail & Related papers  (2022-12-19T14:48:54Z)
• Message Passing Neural PDE Solvers [60.77761603258397]
  We build a neural message passing solver, replacing allally designed components in the graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.
  arXiv  Detail & Related papers  (2022-02-07T17:47:46Z)
• Physics-Informed Neural Operator for Learning Partial Differential Equations [55.406540167010014]
  PINO is the first hybrid approach incorporating data and PDE constraints at different resolutions to learn the operator. The resulting PINO model can accurately approximate the ground-truth solution operator for many popular PDE families.
  arXiv  Detail & Related papers  (2021-11-06T03:41:34Z)
• Semi-Implicit Neural Solver for Time-dependent Partial Differential Equations [4.246966726709308]
  We propose a neural solver to learn an optimal iterative scheme in a data-driven fashion for any class of PDEs. We provide theoretical guarantees for the correctness and convergence of neural solvers analogous to conventional iterative solvers.
  arXiv  Detail & Related papers  (2021-09-03T12:03:10Z)
• dNNsolve: an efficient NN-based PDE solver [62.997667081978825]
  We introduce dNNsolve, that makes use of dual Neural Networks to solve ODEs/PDEs. We show that dNNsolve is capable of solving a broad range of ODEs/PDEs in 1, 2 and 3 spacetime dimensions.
  arXiv  Detail & Related papers  (2021-03-15T19:14:41Z)
• Optimizing Wireless Systems Using Unsupervised and Reinforced-Unsupervised Deep Learning [96.01176486957226]
  Resource allocation and transceivers in wireless networks are usually designed by solving optimization problems. In this article, we introduce unsupervised and reinforced-unsupervised learning frameworks for solving both variable and functional optimization problems.
  arXiv  Detail & Related papers  (2020-01-03T11:01:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.