# Using Neural Networks to Compute Approximate and Guaranteed Feasible Hamilton-Jacobi-Bellman PDE Solutions

arXiv: https://arxiv.org/abs/1611.03158 · HTML: https://mlsanity.com/paper/1611.03158/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2016.

## Built on by (most cited first, 5 of 5)

- [SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problems](https://mlsanity.com/paper/2201.05475/) (2022)
- [Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU](https://mlsanity.com/paper/2604.07644/) (2026)
- [Deep neural network approximation for high-dimensional parabolic Hamilton-Jacobi-Bellman equations](https://mlsanity.com/paper/2103.05744/) (2021)
- [Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs](https://mlsanity.com/paper/2105.03336/) (2021)
- [Formal Safety Verification and Refinement for Generative Motion Planners via Certified Local Stabilization](https://mlsanity.com/paper/2509.19688/) (2025)

## Abstract (arXiv)

To sidestep the curse of dimensionality when computing solutions to Hamilton-Jacobi-Bellman partial differential equations (HJB PDE), we propose an algorithm that leverages a neural network to approximate the value function. We show that our final approximation of the value function generates near optimal controls which are guaranteed to successfully drive the system to a target state. Our framework is not dependent on state space discretization, leading to a significant reduction in computation time and space complexity in comparison with dynamic programming-based approaches. Using this grid-free approach also enables us to plan over longer time horizons with relatively little additional computation overhead. Unlike many previous neural network HJB PDE approximating formulations, our approximation is strictly conservative and hence any trajectories we generate will be strictly feasible. For demonstration, we specialize our new general framework to the Dubins car model and discuss how the framework can be applied to other models with higher-dimensional state spaces.