## 1 Introduction  
With the rapid development of aerospace technology, there has been an increasing demand for low-Earth-orbit micro-satellites to observe multiple targets during short arc segments continuously. The satellite is expected to quickly complete a large-angle agile attitude maneuver control for multi-target observation within a limited time frame. Such an agile attitude maneuver control for micro-satellites is typically achieved through large torque actuators like control moment gyroscopes (CMGs). On the other hand, research to improve the velocity of attitude maneuvering from a control algorithmic perspective is essential. In the realm of controlling uncertain systems, the variable-structure sliding mode control has been the focus of research due to its high robustness and low dependence on model parameters. Therefore, it has found extensive application and development in controlling non-linear systems, such as robots [1], chaos systems [2], aerospace [3; 4; 5], and motors [6; 7]. However, traditional sliding mode control faces serious issues of buffeting. In practical satellite attitude systems, buffeting not only causes energy waste, but also easily stimulates the flexible part of the satellite to oscillate, reducing the accuracy and stability of attitude control, and even leading to the failure of attitude control tasks. This has posed several difficulties for the application of sliding mode control. Therefore, how to mitigate or even eliminate buffeting has always been a focal point. In order to suppress or eliminate buffeting, scholars have proposed methods such as boundary layer methods [8], terminal sliding mode control [9; 10; 11], high-order sliding mode control [12; 13], and control methods based on reaching laws [14; 15; 16; 17; 18]. The boundary layer method employs saturation or continuous functions to replace the sign function, allowing the system to stay around the sliding mode plane. While this reduces buffeting, it also compromises control accuracy. High-order sliding mode control effectively eliminates buffeting, but obtaining the first derivative of the sliding variable is challenging. Terminal sliding mode control and reaching-law-based methods have similar mathematical structures, where the former focuses on the system's motion on the sliding mode plane, and the latter concentrates on the system's motion during the convergence phase. Current reaching laws are grouped into four types: constant-velocity reaching laws, exponential reaching laws, power-reaching laws, and general reaching laws. These have laid the foundation for the design of future reaching laws. Constant-velocity and exponential reaching laws encounter buffeting issues when the system reaches the sliding mode plane. Power reaching laws theoretically eliminate buffeting but have a slower convergence rate when distant from the sliding mode plane. In [19], the authors suggested fast power reaching laws, which combine exponential and power reaching laws to compensate for these defects. Moreover, in ref. [20], dual power reaching laws were introduced, further accelerating the approaching rate when far from the sliding mode plane. Additionally, ref. [21] developed a multi-power-reaching law that divides the approach phase into four stages, each featuring a high approaching rate. In [22], the authors designed a dual power composite function reaching law based on the final function, using the properties of the final function to speed up the approaching rate further. This paper proposes a sliding mode variable-structure control method for satellite attitude maneuver based on piecewise power-law convergence law, aiming at the problem of multi-target-observation attitude maneuver control in the short arc segment of low-orbit satellites. This reaching law uses 1 as the dividing point to separate the convergence process into two phases. Utilizing the properties of power functions, the system has a substantial convergence rate in both phases, and the reaching law becomes zero at the equilibrium point.