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Port-Hamiltonian Based Control of the Sun-Earth 3D Circular Restricted Three-Body Problem: Stabilization of the L1 Lagrange Point

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Document pages: 12 pages

Abstract: In this paper, we usePort-Hamiltonian framework to stabilize the Lagrange points in the Sun-Earth three-dimensional Circular Restricted Three-BodyProblem (CRTBP). Through rewriting the CRTBP into Port-Hamiltonian framework,we are allowed to design the feedback controller through energy-shapingand dissipation injection. The closed-loop Hamiltonian is a candidate of the Lyapunov function to establishnonlinear stability of the designed equilibrium, which enlarges the applicationregion of feedback controller compared with that based on linearized dynamics.Results show that thePort-Hamiltonian approachallows us to successfully stabilize the Lagrange points, where the LinearQuadratic Regulator (LQR) may fail. The feedback system based on Port-Hamiltonian approach is also robust against whitenoise in the inputs.

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