空间飞行器大角度姿态机动混合H2/H∞控制

Mixed H2/H∞ control of spacecraft large angle attitude maneuvers

摘要:

提出一种基于平方和优化的空间飞行器大角度姿态机动混合H₂/H∞控制方法.为适应飞行器大角度姿态机动的要求,采用修正的Rodrigues参数描述卫星的姿态运动,并将飞行器姿态运动学和动力学方程转化为线性参数可变(LPV)系统;为降低设计的保守性,通过引入附加松弛变量,提出一种系统矩阵与Lyapunov矩阵分离的混合H₂/H∞性能准则;基于该性能准则,运用Lyapunov方法和平方和优化技术,推导出飞行器大角度姿态机动混合H₂/H∞状态反馈控制器存在的充分条件,并将混合H₂/H∞控制器设计问题转化为具有平方和约束的参数优化问题.

Abstract:

A novel approach to mixed H₂/H∞ control of spacecraft large angle attitude maneuvers is proposed based on sum of squares (SOS) optimization. By using modified Rodrigues parameters, the attitude dynamics of the spacecraft is represented in terms of linear parameter varying (LPV) systems. To reduce the designed conservativeness, a new mixed H₂/H∞ performance criterion is presented by introducing additional slack matrix variables, which eliminates the coupling terms between system matrices and Lyapunov matrix. Based on this, a sufficient condition for the existence of mixed H₂/H∞ controller is derived by using Lyapunov approach and SOS optimization. Finally, the H₂/H∞ controller design problem is converted into a parameter optimization problem with SOS constraints.