A Floquet Mode LQR for Orbital Station-Keeping in Cislunar Space

Abstract

A linear optimal control law for orbital station-keeping in the Earth-Moon Restricted Three Body Problem (R3BP) is developed via Linear Quadratic Regulator (LQR) theory. First, the cost function is established considering a periodic state-weight matrix, leveraging stability information of the target orbits retrieved through Floquet theory. Then, the resulting periodic Riccati differential equation is solved and local asymptotic stability guarantees are shown. Finally, the performance of the proposed LQR when tracking periodic orbits in the circular and elliptic R3BPs is analyzed numerically.