This article explores an adaptive robust control scheme for satellite formation-containment flying in a way of constraint following. For safe flight and uncertainty suppression, both collision avoidance and uncertainty suppression are addressed. First, for uncertainty suppression, (possibly fast) time-varying but bounded uncertainty is considered, and then an adaptive law is proposed to estimate the comprehensive uncertainty bounds online. Second, the problem of formation-containment control with collision avoidance is converted into another problem of constraint-following control by taking the objectives of collision avoidance, formation, and containment, respectively, as the collision-avoidance constraint, formation constraint, and containment constraint. Third, an $\eta $ -measure is introduced to gauge the constraint-following error, and then an adaptive robust control is proposed to render the error to be uniformly bounded and uniformly ultimately bounded, regardless of the uncertainty. By this, the satellites can follow the above collision-avoidance constraint, formation constraint, and containment constraint approximately. As a result, satellite formation-containment control emphasis on collision avoidance and uncertainty suppression is achieved.

中文翻译：

---

卫星编队遏制控制重点是避免碰撞和抑制不确定性

本文探讨了一种约束跟随方式的卫星编队遏制飞行的自适应鲁棒控制方案。为了安全飞行和不确定性抑制，避免碰撞和不确定性抑制都得到解决。首先，对于不确定性抑制，考虑（可能是快速的）时变但有界的不确定性，然后提出自适应律来在线估计综合不确定性界限。其次，将避碰编队遏制控制问题转化为约束跟随控制问题，将避碰、编队、遏制目标分别作为避碰约束、编队约束、遏制约束。第三，一个 $\eta$ 引入测量来测量约束跟随误差，然后提出自适应鲁棒控制以使误差均匀有界并且最终均匀有界，而不管不确定性如何。这样，卫星就可以近似地遵循上述避碰约束、编队约束和遏制约束。从而实现了强调避免碰撞和抑制不确定性的卫星编队遏制控制。