# Receding Hamiltonian-Informed Optimal Neural Control and State Estimation for Closed-Loop Dynamical Systems

arXiv: https://arxiv.org/abs/2411.01297 · HTML: https://mlsanity.com/paper/2411.01297/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 2 Nov 2024.

## Builds on (most cited first, 7 of 7)

- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [Learning an Approximate Model Predictive Controller with Guarantees](https://mlsanity.com/paper/1806.04167/) (2018)
- [Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms](https://mlsanity.com/paper/2203.07747/) (2022)
- [Physics-Informed Neural Nets for Control of Dynamical Systems](https://mlsanity.com/paper/2104.02556/) (2021)
- [Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators](https://mlsanity.com/paper/2109.10793/) (2021)
- [Physics-informed neural networks for PDE-constrained optimization and control](https://mlsanity.com/paper/2205.03377/) (2022)
- [Fast Physics-Informed Model Predictive Control Approximation for Lyapunov Stability](https://mlsanity.com/paper/2410.16173/) (2024)

## Abstract (arXiv)

This paper formalizes Hamiltonian-Informed Optimal Neural (Hion) controllers, a novel class of neural network-based controllers for dynamical systems and explicit non-linear model-predictive control. Hion controllers estimate future states and develop an optimal control strategy using Pontryagin's Maximum Principle. The proposed framework, along with our Taylored Multi-Faceted Approach for Neural ODE and Optimal Control (T-mano) architecture, allows for custom transient behavior, predictive control, and closed-loop feedback, addressing limitations of existing methods. Comparative analyses with established model-predictive controllers revealed Hion controllers' superior optimality and tracking capabilities. Optimal control strategies are also demonstrated for both linear and non-linear dynamical systems.