Lyapunov Differential Equation Approach to Elliptical Orbital Rendezvous with Constrained Controls

作者：Zhou, Bin^*; Lin, Zongli; Duan, Guang-Ren

来源：Journal of Guidance, Control, and Dynamics, 2011, 34(2): 345-358.

DOI：10.2514/1.52372

• INPUT SATURATION
• FEEDBACK-CONTROL
• SYSTEMS SUBJECT
• THRUST
• SPACECRAFT
• GUIDANCE
• DESIGN
• MOTION
• STABILIZATION
• NAVIGATION

This paper is concerned with spacecraft rendezvous with target spacecraft in an arbitrary elliptical orbit. With three independent control accelerations being the control of the resulting linearized Tschauner-Hempel equations, the spacecraft rendezvous problem can be reformulated as a regulation problem with controls of bounded magnitude and energy. A parametric Lyapunov differential equation approach is proposed in this paper to solve this constrained regulation problem. After establishing the fact that the Tschauner-Hempel equations are both null controllable with controls of bounded magnitude and energy, this paper proves that the proposed linear periodic controller semiglobally stabilizes the system. Equivalently, for any fixed initial conditions, the magnitude and energy of the control can be made as small as desired by tuning some free parameters in the feedback laws. In comparison with the existing quadratic-regulation-based approach, which requires solutions to nonlinear Riccati differential equations, the new approach requires only the solution of linear periodic Lyapunov differential equations, which are investigated in the paper by using the periodic generator approach. Numerical simulations of the nonlinear model of the spacecraft rendezvous instead of a linearized one show that both the magnitude and energy of the control can be reduced to an arbitrarily small level by reducing the values of some parameters in the controller and that the rendezvous mission can be accomplished satisfactorily.

• 出版日期2011-4
• 单位哈尔滨工业大学