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 — Oak Academic Publishing
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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
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 ener gy-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 th e Port-Hamiltonian a pproach 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 whit e noise in the inputs.
KeywordsPort-HamiltonianLagrange PointsCircular Restricted Three-Body Problem (CRTBP)Linear Quadratic Regulator (LQR)
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