In this study, a two-step control methodology is developed for energy-optimal reconfiguration of satellites in formation in the presence of uncertainties or external disturbances. First, based on a linear deterministic system model, an optimal control law is analytically determined such that a satellite maneuvers from an initial state to a final state relative to another satellite. The structure of this optimal solution is predetermined and simply given by a linear combination of the fundamental matrix solutions associated with the original equations of relative motion. Only the coefficients are to be determined to satisfy given initial and final conditions. In the second step, an uncertain nonlinear formation system is considered and a robust adaptive controller is designed to compensate for the effects of uncertainties or disturbances that the formation system may encounter. Although the control strategy is inspired by sliding mode control, it produces smooth control signals, thereby avoiding chattering. Also, an adaptation law is added such that the uncertainty or disturbance effects are effectively and quickly eliminated without a priori information about them. The combination of these two controllers guarantees that the satellite accurately tracks the optimal path in the unknown environment. Numerical simulations demonstrate the effectiveness and accuracy of the proposed two-step control methodology, in which a satellite formation is optimally reconfigured under unknown environmental disturbances.

在这项研究中，开发了一种两步控制方法，用于在存在不确定性或外部干扰的情况下，对编队中的卫星进行能量优化配置。首先，基于线性确定性系统模型，分析确定最佳控制律，以使卫星相对于另一颗卫星从初始状态操纵到最终状态。该最优解的结构是预先确定的，并通过与原始相对运动方程式关联的基本矩阵解的线性组合简单给出。仅确定系数以满足给定的初始和最终条件。第二步 考虑了不确定的非线性地层系统，并设计了鲁棒的自适应控制器来补偿地层系统可能遇到的不确定性或干扰的影响。尽管控制策略是受滑模控制启发的，但它会产生平滑的控制信号，从而避免抖动。而且，添加了适应定律，从而可以有效，快速地消除不确定性或干扰影响，而无需先验信息。这两个控制器的组合可确保卫星准确地跟踪未知环境中的最佳路径。数值模拟证明了所提出的两步控制方法的有效性和准确性，其中，在未知环境干扰下，卫星编队被最佳地重新配置。