零角动量欠驱动航天器逆最优稳定控制律设计

研究轮控式零角动量欠驱动航天器姿态最优稳定控制问题。考虑到该类型航天器不存在定常光滑稳定控制律的特点，通过Lyapunov直接法和Backstepping方法设计了一种非线性不连续反馈控制律，同时得到控制Lyapunov函数（CLF），并由此得到逆最优稳定控制律。该控制律可以避开求解Hamilton-Jacobi方程，最小化某一代价函数，同时具有扇形稳定裕度，对输入不确定性具有一定的鲁棒性。数学仿真结果表明，所设计的非线性不连续反馈控制律能够使姿态渐近稳定至平衡点，并具有最优性，以及在转动惯量存在不确定性时，扇形稳定裕度使系统具有一定的鲁棒性。

Inverse Optimal Stabilization of an Underactuated Spacecraft in a Zero Angular Momentum Mode

The problems of optimal stabilization of an underactuated spacecraft using two wheels in a zero angular momentum mode are investigated in this paper. Considering this kind of spacecraft cannot be stabilized by time-invariant smooth control laws, a nonlinear discontinuous control law is designed based on the Lyapunov direct method and the backstepping technique. Then an inverse optimal control law is presented which circumvents the task of solving the Hamilton-Jacobi equation and minimizes a meaningful cost function using control Lyapunov function (CLF). A consequence of the optimality is that the control law has a sector margin which guarantees robustness with respect to input uncertainties. The simulation results show the asymptotical stability and the optimality of the proposed control law. In addition, the sector margin guarantees robustness when the moments of inertia are of uncertainty.