## 1 Introduction  
Earth observation (EO) is the information gathering of Earth's physical, chemical, and biological systems by the use of remote sensing technologies. EO with satellites has been implemented in many different areas, such as weather forecasting, natural disaster monitoring, natural resources management, land-use change measurement, and others [1; 2]. However, when facing some emergency services, it is a challenge for current EO satellites to complete the target information acquisition and transmission in a short time [3], for the actual performance of task execution in EO missions with traditional satellites is limited by several factors, like short communication windows between satellites and ground stations, low data transmitting rates from satellites to ground, and large amounts of image data [4]. It means that the contemporary work mode of EO satellites is difficult to meet the requirements of the complex future EO situations, especially in some emergency situations. Fortunately, with the great improvement of satellite technology in recent years [5; 6], especially in areas of nano-satellites, low-cost rockets, and launch methods, satellite clusters, as a new space system for future space missions, has attracted a lot of attention. Similar to mobile wireless sensor networks (MWSNs) [7], satellite cluster networks (SCNs) is a self-organizing distributed satellite system, in which several cooperatively-working satellites work together to accomplish the complex space mission through wireless inter-satellites links [8]. Thoughthis conception of SCNs with cooperative work has been advanced long before, it has been ignored because of the limitation of high cost of satellites' research and development. In 1991, [PERSON] et al. [9, 10] analyzed the system load and traffic distribution of SCNs based on an exact Markov modeling, and established a mathematical model of network capacity. In recent years, due to the development of satellites technologies, like miniaturization and highly integration, researchers re-focused their minds on the research of SCNs. [PERSON] et al. [11] took the SCNs with fifteen satellites in geosynchronous orbit (GSO) as the research object, figuring out that the hybrid architecture realizes a stunning trade-off between the network efficiency and robustness. [PERSON] et al. [12] analyzed the characteristics of the distributed satellite cluster network and proposed a power control approach based on presetting prediction. For problems in task scheduling, a predictive-reactive scheduling model has been proposed using the hybrid of periodic task scheduling and dynamic adjustment [13]. Though some technical problems in SCNs have been widely researched, the technique of topology control strategy in SCNs is still immature and there are only a few studies focused on it. Topology control strategies are included in network management techniques. Because of the unstable inter-satellites links (ISLs) in SCNs and the possible data transmitting errors among satellites, the main goal of topology control in SCNs is to achieve the most stable data routing paths for the cooperative-working satellites. However, topology control strategy, as one of the key technologies in SCNs, has seldom been studied in recent years [14, 15]. In 2016, [PERSON] et al. [16] proposed logical \(k\)-connected topology control algorithms, including both the purely centralized and the purely distributed, but it mainly focuses on a hierarchical integrated network which include not only SCNs, also the unmanned aerial vehicles (UAVs) and WSNs. And the algorithms take the satellites in one cluster as a node, and do not establish the inner topology of the cluster. In other research areas, UAVs and MWSNs, network topology control techniques for mobile self-organization networks have been deeply researched [17, 18, 19].