# Real-time optimal control via Deep Neural Networks: study on landing problems

arXiv: https://arxiv.org/abs/1610.08668 · HTML: https://mlsanity.com/paper/1610.08668/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2016.

## Built on by (most cited first, 28 of 28)

- [Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints](https://mlsanity.com/paper/2507.08124/) (2025)
- [Neural representation of a time optimal, constant acceleration rendezvous](https://mlsanity.com/paper/2203.15490/) (2022)
- [Learning the optimal state-feedback via supervised imitation learning](https://mlsanity.com/paper/1901.02369/) (2019)
- [On the Universal Transformation of Data-Driven Models to Control Systems](https://mlsanity.com/paper/2102.04722/) (2021)
- [Advances in Trajectory Optimization for Space Vehicle Control](https://mlsanity.com/paper/2108.02335/) (2021)
- [Selected Trends in Artificial Intelligence for Space Applications](https://mlsanity.com/paper/2212.06662/) (2022)
- [Co-Optimizing Reconfigurable Environments and Policies for Decentralized Multi-Agent Navigation](https://mlsanity.com/paper/2403.14583/) (2024)
- [Optimality Principles in Spacecraft Neural Guidance and Control](https://mlsanity.com/paper/2305.13078/) (2023)
- [Real-time optimal control of high-dimensional parametrized systems by deep learning-based reduced order models](https://mlsanity.com/paper/2409.05709/) (2024)
- [PINNIES: An Efficient Physics-Informed Neural Network Framework to Integral Operator Problems](https://mlsanity.com/paper/2409.01899/) (2024)
- [KANtrol: A Physics-Informed Kolmogorov-Arnold Network Framework for Solving Multi-Dimensional and Fractional Optimal Control Problems](https://mlsanity.com/paper/2409.06649/) (2024)
- [Neural Network Optimal Feedback Control with Guaranteed Local Stability](https://mlsanity.com/paper/2205.00394/) (2022)
- [Neural network optimal feedback control with enhanced closed loop stability](https://mlsanity.com/paper/2109.07466/) (2021)
- [Fast solver for J2-perturbed Lambert problem using deep neural network](https://mlsanity.com/paper/2201.02942/) (2022)
- [Optimisation of Structured Neural Controller Based on Continuous-Time Policy Gradient](https://mlsanity.com/paper/2201.06262/) (2022)
- [Feasible Low-thrust Trajectory Identification via a Deep Neural Network Classifier](https://mlsanity.com/paper/2202.04962/) (2022)
- [Certifying Guidance & Control Networks: Uncertainty Propagation to an Event Manifold](https://mlsanity.com/paper/2410.03729/) (2024)
- [Deep L1 Stochastic Optimal Control Policies for Planetary Soft-landing](https://mlsanity.com/paper/2109.00183/) (2021)
- [Space Non-cooperative Object Active Tracking with Deep Reinforcement Learning](https://mlsanity.com/paper/2112.09854/) (2021)
- [Efficient low-thrust trajectory data generation based on generative adversarial network](https://mlsanity.com/paper/2209.06427/) (2022)
- [Jacobian-Enhanced Neural Networks](https://mlsanity.com/paper/2406.09132/) (2024)
- [Latent feedback control of distributed systems in multiple scenarios through deep learning-based reduced order models](https://mlsanity.com/paper/2412.09942/) (2024)
- [Comparing Behavioural Cloning and Reinforcement Learning for Spacecraft Guidance and Control Networks](https://mlsanity.com/paper/2507.19535/) (2025)
- [GCImOpt: Learning efficient goal-conditioned policies by imitating optimal trajectories](https://mlsanity.com/paper/2604.22724/) (2026)
- [Pretrained Approximators for Low-Thrust Trajectory Cost and Reachability](https://mlsanity.com/paper/2605.26790/) (2026)
- [Agentic AutoResearch forSpace Autonomy: An Auditable, LLM-Driven Research Agent for Aerospace Control Problems](https://mlsanity.com/paper/2606.20394/) (2026)
- [Optimality-Informed Neural Networks for Lunar Landing Trajectory Optimization](https://mlsanity.com/paper/2607.02741/) (2026)
- [Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics](https://mlsanity.com/paper/2607.28939/) (2026)

## Abstract (arXiv)

Recent research on deep learning, a set of machine learning techniques able to learn deep architectures, has shown how robotic perception and action greatly benefits from these techniques. In terms of spacecraft navigation and control system, this suggests that deep architectures may be considered now to drive all or part of the on-board decision making system. In this paper this claim is investigated in more detail training deep artificial neural networks to represent the optimal control action during a pinpoint landing, assuming perfect state information. It is found to be possible to train deep networks for this purpose and that the resulting landings, driven by the trained networks, are close to simulated optimal ones. These results allow for the design of an on-board real time optimal control system able to cope with large sets of possible initial states while still producing an optimal response.