## 1 Introduction
[21] considered the data transmission in a discrete-time communication network. In order to adapt to this more realistic engagement situation, the time-estimation method was refined into a discretized form. However, the works proposed above focused on cooperative guidance against fixed targets or nonameuvering targets [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]. Less research has been conducted on cooperative guidance against maneuvering targets [22, 23, 24, 25]. [PERSON] et al. [22] designed an extended state observer (ESO) in both directions to estimate the uncertain disturbance caused by target maneuvers. In [23], to ensure the fast convergence of the time-to-go and reduce the impact of disturbances, super-twisting sliding-mode control was applied in LOS-direction guidance. [PERSON] et al. [24] designed a fixed-time consensus protocol, which further improved the convergence rate of time. [PERSON] et al. [25] proposed a distributed-model predictive-control-guidance law with the virtual-leader method to solve the three-dimensional cooperative-interception problem. Nevertheless, to the best of the authors' knowledge, the multidirection-guidance method in the existing works controls the impact time individually. The impact angle of each vehicle is settled before launch, which prevents autonomous coordination. As an effective tactic, encirclement guidance has received significant attention in recent years. Different methods have been proposed for surrounding the target from multiple angles. [PERSON] et al. [26] propose a distributed cooperative encirclement hunting guidance law for multiple vehicles based on time-varying formation-tracking-control theories. However, the vehicles in [26] cannot attack the target simultaneously. In [27], encirclement interception for a fixed target is realized by a biased proportional-based guidance law. In light of the aforementioned observations, this paper comes up with a novel cooperative-guidance law with a constrained impact angle and simultaneous attack. The main contributions of this paper are as follows:  
* Compared with other cooperative-guidance laws [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21] and encirclement-interception methods [27] that are aimed at a stationary target, this paper presents a new way to realize encirclement interception against a maneuvering target by utilizing a leader-follower topology. During the interception, the followers are arranged around the leader. The vehicles are separated by fixed LOS angles. The guidance law for the lead ers is designed to intercept the target at a certain impact angle. Meanwhile, the cooperative guidance law for the followers is designed with variable LOS-angle constraints;
* A fixed-time distributed disturbance observer (DDOB) was designed to compensate for the insufficient target-maneuver information involved in the guidance law. Compared with the traditional disturbance observer in [22], our distributed disturbance observer has a better performance in distributed cooperative interception;
* A predefined-time consensus guidance (PTCG) law was designed to control the impact angle of the vehicles. Compared with [22; 23; 24; 25], the proposed PTCG introduces the communication-consistency control into the guidance law in the normal direction of the LOS, which improves the adaptive-control ability. Furthermore, the proposed PTCG can ensure that the LOS angles of the followers converge to the desired values in the prescribed time. The convergence time is set as the total flight time, which reduces the control input saturation. The remainder of this paper is organized as follows. Some necessary preliminary knowledge is provided in Section 2. The problem formulation is presented in Section 3. Section 4 presents the design of our cooperative-guidance law and the stability analysis. Numerical simulations are provided in Section 5 to demonstrate its effectiveness and superiority. Finally, conclusions are presented in Section 6.