ABSTRACT In this paper, the problem of robust control for non-cooperative rendezvous is investigated based on implicit Lyapunov function (ILF) method. The dynamical model of relative motion between two spacecrafts is established in the body coordinate system of the chaser spacecraft without using the target-orbital information. In view of unknown inertia parameters and external disturbances, an ILF control-observer scheme is introduced, where the ideal controller is first designed and then estimated by the observer. The closed-loop system is proved to be finite-time stable, and the controller and observer gains are, respectively, obtained by solving linear matrix inequalities and parameterised nonlinear matrix inequalities. To reduce the computational burden, analytical solutions to these matrix inequalities are provided. The effectiveness of the theoretical results is demonstrated by simulation examples.

中文翻译：

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惯性参数未知的非合作交会的 ILF 控制观测器方案中矩阵不等式的解析解

摘要 在本文中，基于隐式李雅普诺夫函数（ILF）方法研究了非合作交会的鲁棒控制问题。在不使用目标轨道信息的情况下，在追逐者航天器的体坐标系中建立了两航天器之间相对运动的动力学模型。针对未知惯性参数和外部扰动，引入ILF控制-观测器方案，首先设计理想控制器，然后由观测器估计。闭环系统被证明是有限时间稳定的，控制器和观测器增益分别通过求解线性矩阵不等式和参数化非线性矩阵不等式获得。为了减少计算负担，提供了这些矩阵不等式的解析解。