Certifying Guidance & Control Networks: Uncertainty Propagation to an Event Manifold
This work provides a novel analytical method for certifying the robustness of neural networks in guidance and control applications, which is crucial for safety-critical systems where Monte Carlo simulations may be insufficient.
This paper develops a method for propagating uncertainty in Guidance & Control Networks (G&CNETs) to an event manifold, enabling the certification of neural networks in optimal control problems. The method analytically describes terminal conditions on an event manifold based on initial state uncertainties, providing confidence bounds using the Cauchy-Hadamard theorem and moment generating functions.
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.