The high-accuracy drag-free control is one of the key technologies for gravity gradient satellites. Since the range of the gravity gradiometer is limited, the measurement is subject to the saturation constraint. This paper introduces a design method of the adaptive drag-free control law by employing the set-valued identification approach. By inserting several thresholds in the constrained interval, the output observation is transformed into the set-valued information under different thresholds, based on which and the weighted optimization technique the identification algorithm for the unknown parameter is constructed. The adaptive drag-free control law is designed via the certainty equivalence principle. It is shown that the identification algorithm is strongly convergent and the convergence rate of the estimation error is obtained. The performance of the closed-loop system is analyzed, and the asymptotic optimality of the adaptive controller is proved. The numerical simulation is included to verify the effectiveness of the main results.

高精度无拖曳控制是重力梯度卫星的关键技术之一。由于重力梯度仪的量程有限，测量受到饱和约束。本文介绍了一种采用设定值辨识方法的自适应无拖曳控制律的设计方法。通过在约束区间内插入多个阈值，将输出观测值转化为不同阈值下的集合值信息，并在此基础上利用加权优化技术构建未知参数的识别算法。自适应无拖曳控制律是根据确定性等价原理设计的。结果表明，辨识算法具有强收敛性，得到了估计误差的收敛速度。分析了闭环系统的性能，证明了自适应控制器的渐近最优性。包括数值模拟以验证主要结果的有效性。