Covariance Control of an Earth-to-Mars Transfer with Control Actuation Errors

This paper presents a convex optimization approach to design a covariance control policy for an interplanetary mission of a spacecraft subject to non-Gaussian control actuation errors. The goal is to develop a closed-loop policy that minimizes the control effort and ensures that the system’s final state aligns with a desired probability distribution. This is achieved by formulating an optimal covariance control problem, which is then transformed into a sequence of deterministic convex optimization problems using state-of-the-art convexification techniques. Two noise models are devised to conveniently incorporate the perturbations in an optimal control framework with low computational complexity. The first is a (conservative) additive white Gaussian noise model, while the second is a more advanced multiplicative noise model, better suited to capture the system’s noise characteristics.