TITLE:
Port-Hamiltonian Based Control of the Sun-Earth 3D Circular Restricted Three-Body Problem: Stabilization of the L1 Lagrange Point
AUTHORS:
Haotian Yan
KEYWORDS:
Port-Hamiltonian, Lagrange Points, Circular Restricted Three-Body Problem (CRTBP), Linear Quadratic Regulator (LQR)
JOURNAL NAME:
Modern Mechanical Engineering,
Vol.10 No.3,
August
31,
2020
ABSTRACT: In this paper, we use
Port-Hamiltonian framework to stabilize the Lagrange points in the Sun-Earth three-dimensional Circular Restricted Three-Body
Problem (CRTBP). Through rewriting the CRTBP into Port-Hamiltonian framework,
we are allowed to design the feedback controller through energy-shaping
and dissipation injection. The closed-loop Hamiltonian is a candidate of the Lyapunov function to establish
nonlinear stability of the designed equilibrium, which enlarges the application
region of feedback controller compared with that based on linearized dynamics.
Results show that the
Port-Hamiltonian approach
allows us to successfully stabilize the Lagrange points, where the Linear
Quadratic Regulator (LQR) may fail. The feedback system based on Port-Hamiltonian approach is also robust against white
noise in the inputs.