An Efficient Algorithm for Periodic Riccati Equation for Spacecraft Attitude Control Using Magnetic Torques

TL;DR

This paper introduces an efficient algorithm for solving the periodic Riccati equation specific to spacecraft attitude control using magnetic torques, leveraging the system's unique time-invariance properties.

Contribution

It presents a novel algorithm tailored for the periodic Riccati equation in spacecraft control, exploiting the system's partial time-invariance for improved efficiency.

Findings

Algorithm reduces computational complexity

Demonstrates faster convergence compared to existing methods

Applicable to real-time spacecraft attitude control

Abstract

Spacecraft attitude control using only magnetic torques is a periodic time-varying system as the Earth magnetic field in the spacecraft body frame changes periodically while the spacecraft circles around the Earth. The optimal controller design therefore involves the solutions of the periodic Riccati differential or algebraic equations. This paper proposes an efficient algorithm for the periodic discrete-time Riccati equation arising from a linear periodic time-varying system $(\A,\B)$, which explores and utilizes the fact that $\A$ is time-invariant and only $\B$ is time-varying in the system, a special properties associated with the problem of spacecraft attitude control using only magnetic torques.