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

TL;DR

This paper develops a method for uncertainty propagation on event manifolds in Guidance & Control Networks, enabling robustness analysis of neural network policies in complex, nonlinear control problems relevant to space and drone applications.

Contribution

It introduces an analytical approach to propagate initial uncertainties on event manifolds for G&CNETs, enhancing certification tools for neural networks in guidance and control.

Findings

Analytical expressions for terminal conditions on event manifolds.

Confidence bounds derived using Cauchy-Hadamard theorem.

Uncertainty propagation performed with moment generating functions.

Abstract

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.