## 1 Introduction  
Earth observation satellites (EOSs) are adopted to take photographs of Earth's surface through their optical and infrared cameras, which are widely used in weather forecasting, environmental protection, and disaster monitoring. Although a large number of EOSs have been launched in recent years, the current EOSs are still struggle to meet the explosively increased observation demands [1; 2; 3]. Therefore, the EOS mission-scheduling, which allocates scarce EOS resources to observation missions, plays a significant role in improving the resource utilization efficiency of the EOS systems. Over the past few decades, extensive research has been conducted on EOS mission-scheduling problems. To obtain an optimal observation plan, some exact algorithms such as the branch and bound algorithm have been proposed for the satellite observation-mission-scheduling problem [4; 5; 6; 7]. As the EOS mission-scheduling problem is a complex non-deterministic polynomial time hard (NP-Hard) problem [8], these exact optimization algorithms struggle to find the optimal solution in a tolerable time in the scheduling scenarios with large-scale missions. Hence, researchers have turned to heuristic algorithms and machine learning algorithms to design the EOS mission-scheduling algorithms. The genetic algorithm (GA) [9; 10; 11], simulated annealing (SA) [12; 13; 14], and ant colony optimization (ACO) [15; 16; 17] have been extensively used to solve the EOS mission-scheduling problem. The local search-based mission-scheduling algorithms such as the simulated annealingalgorithm and neighborhood search algorithm [18; 19; 20] are also popular in solving the EOS mission-scheduling problem. In addition, some learning-based EOS mission-scheduling algorithms based on deep neural networks [21; 22; 23] and deep reinforcement learning [24; 25; 26] have been proposed recently. The existing EOS mission-scheduling algorithms mainly focus on static observation missions, which are submitted before the beginning of the scheduling period. Recently, with the expansion of observation applications such as dynamic observation requests from mobile terminals and dynamic target monitoring [27; 28; 29], the demand for real-time Earth observation information is urgent and enormous. These real-time observation demands, which arrive dynamically during the scheduling horizon and require being performed within a short deadline, are usually defined as dynamic observation missions [30]. Compared with static missions, the profit of dynamic observation missions is higher and dynamic missions have an urgent deadline constraint for observation [30; 31; 32]. In recent years, the scheduling of dynamic observation missions, referred to as dynamic scheduling, has become a hot research topic [33; 34; 35; 36; 37]. [PERSON] et al. proposed a hybrid ACO method combined with iteration local search (ACO-ILS) for the satellite mission-scheduling problem with emergency and common missions [33]. For the distributed imaging satellite constellation, [PERSON] et al. proposed a satellite dynamic scheduling algorithm based on deep reinforcement learning [34]. In addition, a transformer-based fast scheduling algorithm [35], a hybrid genetic tabu search algorithm [36], and a two-phase mission-planning method [37] are proposed for the dynamic mission-scheduling problem. In dynamic scheduling, the perturbation is an important indicator used to measure the difference between the scheduling plan generated by dynamic scheduling and the initial scheduling plan. Although the perturbation directly affects the stability of the EOS system, most of the existing studies on the dynamic observation-mission-scheduling problem ignore perturbations. To the best of our knowledge, only [PERSON] et al. [38] and [PERSON] et al. [39] have investigated the dynamic observation-mission-scheduling problem considering the perturbation. [PERSON] et al.