## 1 Introduction  
In 2015, the LIGO (Laser Interferometer gravitational-wave Observation) team detected gravitational waves for the first time, ushering in a new era of exploring gravitational waves in the universe [1]. The LISA (Laser Interferometer Space Antenna) mission proposed jointly by ESA and NASA consists of three spacecraft deployed on a heliocentric orbit, aiming to detect space-based gravitational wave sources in the frequency range of 0.1 mHz to 1 Hz [2]. Similar to LISA, the TianQin project plans to deploy three spacecraft in Earth's orbit at an altitude of approximately 100,000 km, forming an equilateral triangle constellation with an arm length of about 170,000 km. By utilizing a telescope system to receive and transmit laser beams, a laser link is established between each pair of spacecraft. The detection of space gravitational waves is achieved by measuring the variation in the distance between two test masses [3]. During gravitational wave detection, the constellation formed by three spacecraft may gradually deviate from the ideal equilateral triangle shape over time due to the influence of celestial gravitational perturbations and initial orbital deviations. This deviation is known as the breathing angle variation. After optimizing the constellation configuration for stability, the TianQin constellation can control the breathing angle variation within a range of \(\pm 0.1^{\circ}\) during each three-month observation window [4]. However, the variation in the breathing angle remains significantly larger than the far-field beam width of the telescope (about 5 \(\upmu\)rad) [5], leading to a misalignment of the lines of sight for the two spacecraft, and thereby affecting the normal detection of gravitational waves. Therefore, to ensure the detection of gravitational waves, the TianQin mission specifies a pointing stability requirement of 10 nrad/Hz\({}^{1/2}\) in the frequency range of 0.1 mHz to 1 Hz [6] and utilizes the pointing mechanism to actively compensate for the breathing angle variation. Currently, in space gravitational wave detection, there are two pointing schemes used to compensate for the breathing angle variation within the TianQin constellation. The first scheme is the whole telescope pointing scheme, which involves using the telescope pointing mechanism to rotate the entire mobile optical subassembly (MOSA, consisting of a telescope, optical bench, gravitational reference sensor, telescope pointing mechanism, supporting structures, etc.) to compensate for angular changes. The second scheme is the in-field pointing scheme [7], which entails designing a rotatable mirror within the optical system of the telescope to compensate for angular changes. However, the second scheme increases the complexity of the telescope's optical design and introduces additional stray light [8], thereby affecting the precision of distance measurement. Therefore, using the whole telescope pointing to compensate for the breathing angle variation becomes a feasible solution. In the whole telescope pointing scheme, the stability of the telescope pointing mechanism is compromised due to the influence of unfavorable conditions, such as model uncertainties, disturbance torque noise, and nonlinear friction. Therefore, it is essential to mitigate the impact of these adverse factors to improve the precision and stability of the telescope pointing system. Currently, for the telescope's high-precision pointing control methods, [PERSON] et al. [9] have employed a combination of robust loop shaping and disturbance observer methods to ensure robust stability across the entire operational range. This approach enhances the performance of precision satellite systems and reduces the servo error by a factor of 3.8. [PERSON] et al. [10], using a stacked recursive neural network adaptive controller, addressed the issue of insufficient control precision, achieving precise pointing requirements at the nanoradian level between satellites and telescopes. [PERSON] et al.