# Analytic Time Reentry Cooperative Guidance for Multi-Hypersonic Glide Vehicles
## 1 Introduction  
Hypersonic glide vehicles (HGVs) have the advantages of fast flight speeds and wide maneuvering ranges. They can effectively achieve the goal of one-hour strategic delivery to the world under the engagement condition, which has important strategic value [1, 2]. With the further development of HGVs, various countries have begun to invest in anti-hypersonic technology research. However, the emergence and development of anti-hypersonic technology will weaken the maneuvering and reentry task-completion performance of a single HGV [3, 4]. For conventional aircraft, multi-aircraft cooperative guidance technology effectively improves the performance of task-completion under the engagement condition. Therefore, in recent years, more and more scholars have focused on the research of multi-hypersonic glider cooperative guidance technology to ensure the rapid and accurate reentry advantage of HGVs [5, 6]. Multi-hypersonic cooperative guidance technology requires high coordination in attack time, especially for high-value fixed targets or slow-moving targets. Time coordination can effectively break through the contested environment, achieve a certain saturation effect, and further improve the task-completion performance of HGVs [7, 8]. Since the reentry maneuvering flight process of an HGV is subject to a variety of constraints, in addition to terminal constraints, state variable constraints, and control variable constraints, it is also necessary to meet \"hard constraints\" including heat flux rate, dynamic pressure, andoverload [9; 10]. In addition, the reentry flight is unpowered and cannot maintain a constant altitude and speed, which poses a certain challenge to the time-cooperative reentry guidance. The traditional cooperative guidance method of conventional aircraft with constant velocity assumption cannot be applied to the study of time-cooperative guidance of multi-hypersonic vehicles [3; 10]. In recent years, some scholars have carried out research on the cooperative guidance of multi-hypersonic vehicle reentry and achieved particular results. [PERSON] et al. [11] first studied the cooperative guidance problem of dual hypersonic gliding missiles. [PERSON] et al. [12] proposed a phased cooperative guidance method that can satisfy both time and attack angle coordination. Similarly, [PERSON] et al. [13] carried out the \"two-stage\" cooperative guidance of the glide phase-end guidance phase and proposed a time-cooperative guidance method in the glide phase. In the end guidance, an improved time-angle guidance law was adopted, considering the requirements of angle and time coordination. [PERSON] et al. [14] designed a two-layer cooperative guidance framework by using the common trajectory length as the coordination variable to realize the static coordination of multi-hypersonic vehicles. By improving the prediction-correction algorithm, [PERSON] et al. [15] continuously corrected the time and accuracy of the impact point and finally achieved a better time-consistent synergy effect. Although the cooperative guidance method based on predictive correction can ensure the accuracy of reentry guidance, it needs to predict the remaining range or remaining flight time in each guidance period to update the guidance command integrally, which requires a large number of calculations. In addition, relevant scholars have introduced convex optimization methods into the study of hypersonic vehicle guidance problems. [PERSON] et al. [16] proposed a variable trust region sequence convex programming algorithm, and an adaptive decision trust region radius accelerated the convergence speed of the algorithm and could complete the reentry trajectory planning online. [PERSON] et al. [17] proposed an improved sequential convex optimization algorithm to solve the problem of precise control of the total reentry flight time to realize the time coordination problem during the glide phase.