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中文摘要：
由于卫星各轴角速度之间是相互耦合的,故当姿态作大角度机动时需要考虑其非线性的动力学特性.此外,表示姿态的运动学微分方程也是非线性的.针对这类非线性系统的控制设计,文章提出了一种采用平方和（SOS）的综合方法.虽然SOS法是一种数值计算的方法,但文中表明设计结果却具有清晰的物理意义.所得的控制律可以视为是非线性版本的PD控制.由于修正Rodrigues参数（MRP）本身特性的关系,控制输入会出现峰值,因而文章提出了一种饱和设计.根据此类姿态系统的无源性本质,可以证明饱和下系统的响应是收敛的.同时,提出了一种利用对角优势的设计思路来减少SOS法的数值误差.SOS法可以求解不容易解析求解的非线性问题,具有广阔的应用前景.
英文摘要：
Because of the coupling effect between the angular velocities of each axis, the nonlinear dynamics of the satellite must be considered for the control of large attitude maneuvers. Besides, the kinematics differential equation of the attitude representation is also nonlinear. The sum-of-squares （SOS） approach was proposed as a synthesis method for the nonlinear control system design. It is shown that the final result of the SOS design has clear physical meanings, though it is a numerical method. In fact, the resulting control law can be viewed as a nonlinear version of the PD control. To avoid the peak value of the control input caused by the intrinsic properties of the MRPs, a saturation design was proposed. The convergence of the time response under saturation can be proved by the passivity nature of the system. A diagonal dominance procedure was also proposed to reduce the numerical errors of the SOS approach. The proposed SOS method can be used to solve analytically unsolvable nonlinear problems and would have a wide area of applications in the near future.
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