# Certifying Guidance & Control Networks: Uncertainty Propagation to an Event Manifold

arXiv: https://arxiv.org/abs/2410.03729 · HTML: https://mlsanity.com/paper/2410.03729/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 30 Sep 2024.

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

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Real-time optimal control via Deep Neural Networks: study on landing problems](https://mlsanity.com/paper/1610.08668/) (2016)
- [On the stability analysis of deep neural network representations of an optimal state-feedback](https://mlsanity.com/paper/1812.02532/) (2018)
- [Neural representation of a time optimal, constant acceleration rendezvous](https://mlsanity.com/paper/2203.15490/) (2022)
- [Revisiting high-order Taylor methods for astrodynamics and celestial mechanics](https://mlsanity.com/paper/2105.00800/) (2021)
- [Guidance and Control Networks with Periodic Activation Functions](https://mlsanity.com/paper/2405.18084/) (2024)
- [EclipseNETs: a differentiable description of irregular eclipse conditions](https://mlsanity.com/paper/2408.05387/) (2024)

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

- [Comparing Behavioural Cloning and Reinforcement Learning for Spacecraft Guidance and Control Networks](https://mlsanity.com/paper/2507.19535/) (2025)

## Abstract (arXiv)

We perform uncertainty propagation on an event manifold for Guidance & Control Networks (G&CNETs), aiming to enhance the certification tools for neural networks in this field. This work utilizes three previously solved optimal control problems with varying levels of dynamics nonlinearity and event manifold complexity. The G&CNETs are trained to represent the optimal control policies of a time-optimal interplanetary transfer, a mass-optimal landing on an asteroid and energy-optimal drone racing, respectively. For each of these problems, we describe analytically the terminal conditions on an event manifold with respect to initial state uncertainties. Crucially, this expansion does not depend on time but solely on the initial conditions of the system, thereby making it possible to study the robustness of the G&CNET at any specific stage of a mission defined by the event manifold. Once this analytical expression is found, we provide confidence bounds by applying the Cauchy-Hadamard theorem and perform uncertainty propagation using moment generating functions. While Monte Carlo-based (MC) methods can yield the results we present, this work is driven by the recognition that MC simulations alone may be insufficient for future certification of neural networks in guidance and control applications.