Port-Hamiltonian Based Control of the Sun-Earth 3D Circular Restricted Three-Body Problem: Stabilization of the <i>L</i><sub>1</sub>Lagrange Point

• 作者: Haotian Yan
• 来源期刊: 现代机械工程(英文)
• 学科: 数学
• 关键词: Port-Hamiltonian Lagrange Points Circular Restricted Three-Body Problem (CRTBP) Linear Quadratic Regulator (LQR)
• 年，卷（期）: 2020,（3）
• 页码范围: 39-49
• 页数: 11页
• 分类号: O17

摘要

In this paper, we use Port-Hamiltonian framework to stabilize the Lagrange <span style="font-family:Verdana;">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 ener</span><span style="font-family:Verdana;">gy-shaping and dissipation injection. The closed-loop Hamiltonian is </span><span style="font-family:Verdana;">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 th</span><span style="font-family:Verdana;">e Port-Hamiltonian</span><span style="font-family:Verdana;"> a</span><span style="font-family:Verdana;">pproach allows us to successfully stabilize the Lagrange points, where the Linear Quadratic Regulator (LQR) may fail. The feedback </span><span style="font-family:Verdana;">system based on Port-Hamiltonian approach is also robust against whit</span><span style="font-family:Verdana;">e noise in the inputs.</span>