# Neural network optimal feedback control with enhanced closed loop stability

arXiv: https://arxiv.org/abs/2109.07466 · HTML: https://mlsanity.com/paper/2109.07466/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 15 Sep 2021.

## Builds on (most cited first, 14 of 14)

- [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)
- [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)
- [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)
- [Learning the optimal state-feedback via supervised imitation learning](https://mlsanity.com/paper/1901.02369/) (2019)
- [QRnet: optimal regulator design with LQR-augmented neural networks](https://mlsanity.com/paper/2009.05686/) (2020)
- [Gradient-augmented Supervised Learning of Optimal Feedback Laws Using State-dependent Riccati Equations](https://mlsanity.com/paper/2103.04091/) (2021)
- [Interplanetary Transfers via Deep Representations of the Optimal Policy and/or of the Value Function](https://mlsanity.com/paper/1904.08809/) (2019)
- [The Quadratic-Quadratic Regulator Problem: Approximating feedback controls for quadratic-in-state nonlinear systems](https://mlsanity.com/paper/1910.03396/) (2019)

## Built on by (most cited first, 1 of 1)

- [Neural Network Optimal Feedback Control with Guaranteed Local Stability](https://mlsanity.com/paper/2205.00394/) (2022)

## Abstract (arXiv)

Recent research has shown that supervised learning can be an effective tool for designing optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of these neural network (NN) controllers is still not well understood. In this paper we use numerical simulations to demonstrate that typical test accuracy metrics do not effectively capture the ability of an NN controller to stabilize a system. In particular, some NNs with high test accuracy can fail to stabilize the dynamics. To address this we propose two NN architectures which locally approximate a linear quadratic regulator (LQR). Numerical simulations confirm our intuition that the proposed architectures reliably produce stabilizing feedback controllers without sacrificing optimality. In addition, we introduce a preliminary theoretical result describing some stability properties of such NN-controlled systems.