失效航天器姿态接管的SDRE微分博弈控制

针对燃料耗尽的失效航天器姿态接管控制问题，提出多颗微卫星协同实现姿态稳定的状态相关黎卡提方程(SDRE)微分博弈控制方法。首先，将姿态接管问题转化为多颗微卫星的微分博弈问题，基于组合航天器的姿态模型和微卫星的性能指标函数建立多颗微卫星的非线性微分博弈模型，微卫星通过独立优化各自的性能指标函数得到控制策略。其次，引入状态相关系数矩阵，将非线性博弈转化为状态相关线性二次型博弈，采用SDRE方法更方便地逼近微卫星的博弈均衡策略。最终通过李雅普诺夫迭代法求解耦合状态相关黎卡提方程组得到微卫星的状态反馈控制器，实现微卫星的自主决策。数值仿真验证了多颗微卫星采用微分博弈控制方法实现姿态接管的有效性和容错性。

Attitude Takeover Control of Failed Spacecraft Using SDRE Based Differential Game Approach

In order to service for failed spacecraft running out of fuel, a SDRE based differential game approach is proposed as an on-line attitude controller to realize attitude takeover control through microsatellites coordination. Firstly, based on the nonlinear attitude dynamics of the combined spacecraft formed by multiple microsatellites and the target spacecraft, and the performance index functions of multiple microsatellites, the multi-microsatellite differential game model is established. The attitude takeover control problem is formulated as a differential game problem among multiple microsatellites, where each microsatellite optimizes individual performance index function to get the control strategy. Secondly, the SDRE method is applied to transform the nonlinear differential game to a state-dependent pseudo-linear quadratic differential game by the state-dependent coefficient matrix. The coupled state-dependent Riccati equations is derived to approximate the Nash equilibrium strategies of microsatellites. The set of the coupled equations can be solved iteratively by using the Lyapunov iterations to obtain the state feedback control of each microsatellite with high accuracy. Finally, the numerical simulations verify the effectiveness and fault tolerance of the SDRE based differential game approach for the attitude takeover control of the failed spacecraft.