Circular orbit spacecraft control at the L4 point using Lyapunov functions

TL;DR

This paper demonstrates how Lyapunov functions can be used to design controllers that stabilize a spacecraft in a circular orbit around the L4 point in the CRTBP, ensuring stability and desired orbital parameters.

Contribution

It introduces a Lyapunov-based control synthesis method for L4 orbit stabilization, with proof of asymptotic stability in the CRTBP.

Findings

Controller achieves stable circular orbit at L4

Asymptotic stability proven using LaSalle's principle

Effective control design for fixed radius and angular momentum

Abstract

The objective of this work is to demonstrate the utility of Lyapunov functions in control synthesis for the purpose of maintaining and stabilizing a spacecraft in a circular orbit around the L4 point in the circular restricted three body problem (CRTBP). Incorporating the requirements of a fixed radius orbit and a desired angular momentum, a Lyapunov function is constructed and the requisite analysis is performed to obtain a controller. Asymptotic stability is proved in a defined region around the L4 point using LaSalle's principle.