# Neural Network Optimal Feedback Control with Guaranteed Local Stability

arXiv: https://arxiv.org/abs/2205.00394 · HTML: https://mlsanity.com/paper/2205.00394/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 48 references that are in the map.
- First posted on arXiv 1 May 2022.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Deep Learning Approximation for Stochastic Control Problems](https://mlsanity.com/paper/1611.07422/) (2016)
- [Adaptive Deep Learning for High-Dimensional Hamilton-Jacobi-Bellman Equations](https://mlsanity.com/paper/1907.05317/) (2019)
- [Real-time optimal control via Deep Neural Networks: study on landing problems](https://mlsanity.com/paper/1610.08668/) (2016)
- [A Neural Network Approach for High-Dimensional Optimal Control Applied to Multi-Agent Path Finding](https://mlsanity.com/paper/2104.03270/) (2021)
- [Mitigating the Curse of Dimensionality: Sparse Grid Characteristics Method for Optimal Feedback Control and HJB Equations](https://mlsanity.com/paper/1507.04769/) (2015)
- [Polynomial approximation of high-dimensional Hamilton-Jacobi-Bellman equations and applications to feedback control of semilinear parabolic PDEs](https://mlsanity.com/paper/1702.04400/) (2017)
- [On the stability analysis of deep neural network representations of an optimal state-feedback](https://mlsanity.com/paper/1812.02532/) (2018)
- [Aggressive Online Control of a Quadrotor via Deep Network Representations of Optimality Principles](https://mlsanity.com/paper/1912.07067/) (2019)
- [Semiglobal optimal feedback stabilization of autonomous systems via deep neural network approximation](https://mlsanity.com/paper/2002.08625/) (2020)
- [SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problems](https://mlsanity.com/paper/2201.05475/) (2022)
- [Learning the optimal state-feedback via supervised imitation learning](https://mlsanity.com/paper/1901.02369/) (2019)
- [HJB Optimal Feedback Control with Deep Differential Value Functions and Action Constraints](https://mlsanity.com/paper/1909.06153/) (2019)
- [QRnet: optimal regulator design with LQR-augmented neural networks](https://mlsanity.com/paper/2009.05686/) (2020)
- [Interplanetary Transfers via Deep Representations of the Optimal Policy and/or of the Value Function](https://mlsanity.com/paper/1904.08809/) (2019)
- [Algorithms of Data Development For Deep Learning and Feedback Design](https://mlsanity.com/paper/1912.00492/) (2019)
- [A Machine Learning Enhanced Algorithm for the Optimal Landing Problem](https://mlsanity.com/paper/2203.06753/) (2022)
- [Neural network optimal feedback control with enhanced closed loop stability](https://mlsanity.com/paper/2109.07466/) (2021)

## Built on by (most cited first, 2 of 2)

- [YANNs: Y-wise Affine Neural Networks for Exact and Efficient Representations of Piecewise Linear Functions](https://mlsanity.com/paper/2505.07054/) (2025)
- [Structured Transformations for Stable and Interpretable Neural Computation](https://mlsanity.com/paper/2508.00127/) (2025)

## Abstract (arXiv)

Recent research shows that supervised learning can be an effective tool for designing near-optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of neural network controllers is still not well understood. In particular, some neural networks with high test accuracy can fail to even locally stabilize the dynamic system. To address this challenge we propose several novel neural network architectures, which we show guarantee local asymptotic stability while retaining the approximation capacity to learn the optimal feedback policy semi-globally. The proposed architectures are compared against standard neural network feedback controllers through numerical simulations of two high-dimensional nonlinear optimal control problems: stabilization of an unstable Burgers-type partial differential equation, and altitude and course tracking for an unmanned aerial vehicle. The simulations demonstrate that standard neural networks can fail to stabilize the dynamics even when trained well, while the proposed architectures are always at least locally stabilizing and can achieve near-optimal performance.