## 1 Introduction  
Recently, the orbital pursuit-evasion problem has attracted increasing attention in space research [1; 2; 3; 4]. This problem can be formulated as a differential game [5], which aims to obtain the optimal control strategy of the pursuer and/or the evader in the worst-case scenario, so as to realize the interception of the evader or the evasion from the pursuer. [PERSON] [6] was regarded as the first person to study the orbital pursuit-evasion problem, he solved the problem of intercepting a maneuverable satellite under the assumption of planar motion and constant gravitational field. Since then, many works have focused on the orbital pursuit-evasion problem. In reference [7], a method based on periodically updating the solution of the two-point boundary value problem (TPBVP) was proposed to generate near optimal feedback controls for the orbital pursuit-evasion problem. However, this method is time-consuming and difficult to be applied in real time. In order to overcome these drawbacks, [PERSON] [8] used a modified first-order differential dynamic programming algorithm to generate near-optimal feedback controls. References [9; 10; 11] found the saddle-point equilibrium solutions of the three-dimensional orbital pursuit-evasion game respectively by three different hybrid numerical methods. [PERSON] et al. [12] applied the sensitivity method to the orbital pursuit-evasion problem, which greatly reduces the computation burden for solving this problem numerically. [PERSON] studied the problem of avoiding an interception and proposed two optimal evasive-maneuver strategies with the impulsive thrust [13] and the continuous low thrust [1] respectively. [PERSON] et al. [14] derived minimum-fuel impulsive strategies for return-on-state maneuvers by applying the primer vector theory. [PERSON] [15] developed the guidance laws for the noisy satellite pursuit-evasion game. [PERSON] et al. [16] studied an incomplete, imperfect information game and presented the adaptive strategies for the pursuer and the evader. [PERSON] et al. [17] developed a near-optimal feedback controller for the two-player pursuit-evasion games by using a new extremal-field approach. The above works were studied in the two-player pursuit-evasion game framework. However, in this framework, the evader can only perform maneuvers by itself to avoid threats. It is called self-defense, which disturbs the original mission of the evader and requires a large additional amount of fuel. To overcome this disadvantage, a defender is introduced in [18]. The role of the defender is intercepting the pursuer. In this way, the evader can perform its original mission without being disturbed. A hybrid method combined particle swarm optimization with a Newton-Interpolation algorithm was proposed to solve the orbital defense problem. However, because of the introduction of the defender, the pursuer must avoid the interception by the defender while capturing the evader [19], which makes the design of the pursuer's control strategy more complicated. In order to develop control strategies for pursuers, [PERSON] et al. [19] proposed a distributed online mission plan algorithm for pursuers to access targets. However, these works on the orbital pursuit-evasion-defense game adopted the impulsive thrust, which suffers the drawback that the interception will fail when the target can perform evasive maneuvers [4]. Compared with the impulse thrust, the continuous low thrust allows players to perform multiple, continuous maneuvers, which meets the requirements of the frequently orbital transfers in the game. When applying the continuous low thrust, the hypothesis about players' maneuverable is removed. It is closer to the actual situation of the orbital pursuit-evasion-defense game. Therefore, in this paper, the orbital pursuit-evasion-defense game model is constructed based on the continuous low thrust. Different from the model based on impulse thrust, the model based on continuous low thrust cannot adopt the Keplerian dynamics [20].