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首页> 外文期刊>Journal of guidance, control, and dynamics >Lyapunov Differential Equation Approach to Elliptical Orbital Rendezvous with Constrained Controls
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Lyapunov Differential Equation Approach to Elliptical Orbital Rendezvous with Constrained Controls

机译：具有约束控制的椭圆轨道交会的Lyapunov微分方程方法

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摘要

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.
机译：本文涉及在任意椭圆轨道上与目标航天器交会的航天器。通过三个独立的控制加速度作为对所得线性化的Tschauner-Hempel方程的控制，可以将航天器的交会问题重新定义为具有有限幅度和能量控制的调节问题。为了解决该约束调节问题，本文提出了一种参数化的Lyapunov微分方程方法。建立Tschauner-Hempel方程都是有限值和能量控制的零可控事实后，本文证明了所提出的线性周期控制器能使系统半全局稳定。同样，对于任何固定的初始条件，通过调整反馈定律中的一些自由参数，可以使控制的大小和能量尽可能小。与现有的基于二次调节的方法相比，该方法需要求解非线性Riccati微分方程，而新方法仅需要线性周期Lyapunov微分方程的求解，本文使用周期生成器方法对此进行了研究。航天器集合点的非线性模型（而不是线性模型）的数值模拟表明，通过减小控制器中某些参数的值，可以将控制的大小和能量降低到任意小的水平，并且可以将集合点任务设为令人满意地完成。

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  • 来源
    《Journal of guidance, control, and dynamics》 |2011年第2期|p.345-358|共14页
  • 作者

    Bin Zhou; Zongli Lin; Guang-Ren Duan;

  • 作者单位

    Harbin Institute of Technology, 150001 Harbin, People's Republic of China,Center for Control Theory and Guidance Technology, P.O. Box 416;

    University of Virginia, Charlottesville, Virginia 22904-4743,Department of Electrical and Computer Engineering, P.O. Box 400743-4743;

    Harbin Institute of Technology, 150001 Harbin, People's Republic of China,Center for Control Theory and Guidance Technology, P.O. Box 416;

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